《高级Web技术》参考资料：1-webapp outline_Planetary-Scale Views on a Large Instant-Messaging Network

Planetary- scale views on a large Instant-Messaging Network Jure leskovec Eric horvitz Carnegie Mellon University Microsoft Research jure@cs. cmu. edu horvitz@microsoft.com ABSTRACT We explore a dataset of 30 billion conversations generated We present a study of anonymized data capturing a month by 240 million distinct users over one month. We found that of high-level communication activities within the whole of approximately 90 million distinct Messenger accounts were the Microsoft Messenger instant-messaging system. We ex accessed each day and that these users produced about 1 bil- amine characteristics and patterns that emerge from the col- lion conversations, with approximately 7 billion exchanged lective dynamics of large numbers of people, rather than the messages per day. 180 million of the 240 million active ac- actions and characteristics of individuals. The dataset con- counts had at least one conversation on the observation pe- tains summary properties of 30 billion conversations among riod. We found that 99% of the conversations occurred be- 240 million people. From the data, we construct a commu- tween 2 people, and the rest with greater numbers of partic nication graph with 180 million nodes and 1.3 billion undi- ants. To our knowledge, our investigation represents the ected edges, creating the largest social network constructed largest and most comprehensive study to date of presence and analyzed to date. We report on multiple aspects of and communications in an IM system. A recent report [6] the dataset and synthesized graph. We find that the graph estimated that approximately 12 billion instant messages are well-connected and robust to node removal. We inves sent each day. Given the estimate and the growth of IM, we estimate that we captured approximately half of the world's tigate on a planetary-scale the oft-cited report that people IM communication during the observation period are separated by "six degrees of separation"and find that the average path length among Messenger users is 6.6. We We created an undirected communication network fro also find that people tend to communicate more with each the data where each user is represented by a node and an other when they have similar age, language, and location edge is placed between users if they exchanged at least one and that cross-gender conversations are both more frequent message during the month of observation. The network rep- nd of longer duration than conversations with the same resents accounts that were active during une 2006. In sum- mary, the communication graph has 180 million nodes, rep- resenting users who participated in at least one conversation Categories and Subject Descriptors: H.2.8 Database and 1.3 billion undirected edges among active users,where Management:: Database applications- Data mining an edge indicates that a pair of people communicated. We General Terms: Measurement; Experimentation note that this graph should be distinguished from a buddy Keywords: Social networks; Communication networks; User raph where two people are connected if they appear on eacl demographics: Large data: Online communication others contact lists. The buddy graph for the data contains 240 million nodes and 9.1 billion edges. On average each 1. INTRODUCTION account has approximately 50 buddies on a contact list To highlight several of our key findings, we discovered that Large-scale web services provide unprecedented opportu- the communication network is well connected, with 99.9% nities to capture and analyze behavioral data on a plan of the nodes belonging to the largest connected component etary scale. We discuss findings drawn from aggregations We evaluated the oft-cited finding by Travers and migra of anonymized data representing one month(June 2006) of high-level communication activities of people using the Mi that any two people are linked to one another on average crosoft Messenger instant-messaging(IM)network. We did via a chain with" 6-degrees-of-separation"[17. We found not have nor seek access to the content of messages. Rather that the average shortest path length in the Messenger net- work is 6.6(median 6), which is half a link more than the we consider structural properties of a communication graph path length measured in the classic study.However, we and study how structure and communication relate to us also found that longer paths exist in the graph, with lengths demographic attributes, such as gender, age, and location The data set provides a unique lens for studying patterns of up to 29. We observed that the network is well clustered, human behavior on a wide scale with a clustering coefficient [19 that decays with exponent -0.37. This decay is significantly lower than the value we Jure Leskovec performed this research during an internship had expected given prior research [11]. We found strong t microsoft research homophily 9, 12 among users; people have more conversa- Copyright is held by the Intemational World Wide Web Conference Com tions and converse for longer durations with people who are mittee(Iw3C2). Distribution of these papers is limited to classroom us similar to themselves. We find the strongest homophily for the language used, followed by conversants' geographic lo- www 2008, April 21-25, 2008, Beijing, China ACM978-1-60558-085-2/08/04

Planetary-Scale Views on a Large Instant-Messaging Network Jure Leskovec ∗ Carnegie Mellon University jure@cs.cmu.edu Eric Horvitz Microsoft Research horvitz@microsoft.com ABSTRACT We present a study of anonymized data capturing a month of high-level communication activities within the whole of the Microsoft Messenger instant-messaging system. We ex￾amine characteristics and patterns that emerge from the col￾lective dynamics of large numbers of people, rather than the actions and characteristics of individuals. The dataset con￾tains summary properties of 30 billion conversations among 240 million people. From the data, we construct a commu￾nication graph with 180 million nodes and 1.3 billion undi￾rected edges, creating the largest social network constructed and analyzed to date. We report on multiple aspects of the dataset and synthesized graph. We find that the graph is well-connected and robust to node removal. We inves￾tigate on a planetary-scale the oft-cited report that people are separated by “six degrees of separation” and find that the average path length among Messenger users is 6.6. We also find that people tend to communicate more with each other when they have similar age, language, and location, and that cross-gender conversations are both more frequent and of longer duration than conversations with the same gender. Categories and Subject Descriptors: H.2.8 Database Management: : Database applications – Data mining General Terms: Measurement; Experimentation. Keywords: Social networks; Communication networks; User demographics; Large data; Online communication. 1. INTRODUCTION Large-scale web services provide unprecedented opportu￾nities to capture and analyze behavioral data on a plan￾etary scale. We discuss findings drawn from aggregations of anonymized data representing one month (June 2006) of high-level communication activities of people using the Mi￾crosoft Messenger instant-messaging (IM) network. We did not have nor seek access to the content of messages. Rather, we consider structural properties of a communication graph and study how structure and communication relate to user demographic attributes, such as gender, age, and location. The data set provides a unique lens for studying patterns of human behavior on a wide scale. ∗ Jure Leskovec performed this research during an internship at Microsoft Research. Copyright is held by the International World Wide Web Conference Com￾mittee (IW3C2). Distribution of these papers is limited to classroom use, and personal use by others. WWW 2008, April 21–25, 2008, Beijing, China. ACM 978-1-60558-085-2/08/04. We explore a dataset of 30 billion conversations generated by 240 million distinct users over one month. We found that approximately 90 million distinct Messenger accounts were accessed each day and that these users produced about 1 bil￾lion conversations, with approximately 7 billion exchanged messages per day. 180 million of the 240 million active ac￾counts had at least one conversation on the observation pe￾riod. We found that 99% of the conversations occurred be￾tween 2 people, and the rest with greater numbers of partic￾ipants. To our knowledge, our investigation represents the largest and most comprehensive study to date of presence and communications in an IM system. A recent report [6] estimated that approximately 12 billion instant messages are sent each day. Given the estimate and the growth of IM, we estimate that we captured approximately half of the world’s IM communication during the observation period. We created an undirected communication network from the data where each user is represented by a node and an edge is placed between users if they exchanged at least one message during the month of observation. The network rep￾resents accounts that were active during June 2006. In sum￾mary, the communication graph has 180 million nodes, rep￾resenting users who participated in at least one conversation, and 1.3 billion undirected edges among active users, where an edge indicates that a pair of people communicated. We note that this graph should be distinguished from a buddy graph where two people are connected if they appear on each other’s contact lists. The buddy graph for the data contains 240 million nodes and 9.1 billion edges. On average each account has approximately 50 buddies on a contact list. To highlight several of our key findings, we discovered that the communication network is well connected, with 99.9% of the nodes belonging to the largest connected component. We evaluated the oft-cited finding by Travers and Milgram that any two people are linked to one another on average via a chain with “6-degrees-of-separation” [17]. We found that the average shortest path length in the Messenger net￾work is 6.6 (median 6), which is half a link more than the path length measured in the classic study. However, we also found that longer paths exist in the graph, with lengths up to 29. We observed that the network is well clustered, with a clustering coefficient [19] that decays with exponent −0.37. This decay is significantly lower than the value we had expected given prior research [11]. We found strong homophily [9, 12] among users; people have more conversa￾tions and converse for longer durations with people who are similar to themselves. We find the strongest homophily for the language used, followed by conversants’ geographic lo-

cations, and then age. We found that homophily does not hold for gender: people tend to converse more frequently and with longer durations with the opposite gender. We also examined the relation between communication and dis- ance and found that the number of conversations tends to decrease with increasing geographical distance between con- versant. However, communication links spanning longer distances tend to carry more and longer conversations (b)AddBuddy 2. INSTANT MESSAGING Figure 1: Distribution of the number of events per The use of IM has been become widely adopted in personal user.(a)Number of logins per user.(b)Number of and businesss communications, im clients allow users fast buddies added per use ear-synchronous communication, placing it between sy chronous communication mediums, such as real-time voi Presence events: These include login, logout interactions, and asynchronous communication mediums like ever login, add, remove and block a buddy, ad email [ 18. IM users exchange short text messages with one registered buddy (invite new user), change of or more users from their list of contacts, who have to be on- (busy, away, be-right-back, idle, etc. ) Events are line and logged into the IM system at the time of interaction and time stamped. As conversations and messages exchanged within them are ually very short, it has been observed that users employ Communication: For each user participating in the informal language session, the log contains the following tuple: session id loose grammar, numerous abbreviations, with minimal punctuation [ 10. Contact lists are commonly ser id, time joined the session, time left the session, number of messages sent, number of messages receive referred to as buddy lists and users on the lists are referred to as buddies User data: For each the following self-reported information is stored: age, gender, location(country, 2.1 Research on instant messaging ZIP), language, and IP address. We use the IP address Several studies on smaller datasets are related to this to decode the geographical coordinates, which we then work. Avrahami and Hudson 3 explored communication e to position users on the globe and to calculate dis- characteristics of 16 IM users. Similarly, Shi et al. 13ana- zed IM contact lists submitted by users to a public website and explored a static contact network of 140,000 people. Re- We gathered data for 30 days of June 2006. Each day cently, Xiao et al. 20] investigated IM traffic characteristics yielded about 150 gigabytes of compressed text logs (4.5 within a large organization with 400 users of Messenger. Or terabytes in total). Copying the data to a dedicated eight- study differs from the latter study in that we analyze the full processor server with 32 gigabytes of memory took 12 hours Messenger population over a one month period, capturing Our log-parsing system employed a pipeline of four threads the interaction of user demographic attributes, communica- that e the data allel, collapse the session join/leave tion patterns, and network structure events into sets of conversations, and save the data in a com- 2.2 Data description pact compressed binary format. This process compressed the data down to 45 gigabytes per day. Processing the data To construct the microsoft instant messenger communica- took an additional 4 to 5 hours per day. tion dataset, we combined three different sources of data:(1) A special challenge was to account for missing and dropped Iser demographic information,(2)time and user stampe events, and session"id recycling"across different IM servers vents describing the presence of a particular user, and ( 3) in a server farm. As part of this process, we closed a session communication session logs, where, for all participants, the 48 hours after the last leave session event. We closed sessions number of exchanged messages and the periods of time spent automatically if only one user was left in the conversation participating in sessions is recorded We use the terms session and conversation interchange- ably to refer to an IM interaction among two or more people. 3. USAGE POPULATION STATISTIcs Ithough the M ger system limits the number We shall first review several statistics drawn from aggre- ple communicating at the same time to 20, people can enter gations of users and their communication activitie d leave a conversation over time. We note that, for large sessions, people can come and go over time, so conversations 3.1 Levels of activity an be long with many different people participating. We Over the observation period, 242, 720, 596 users logged into observed some very long sessions with more than 50 partic- Messenger and 179, 792, 538 of these users were actively en- ipants joining over time gaged in conversations by sending or receiving at least one All of our data was anonymized; we had no access to per- IM message. Over the month of observation, 17, 510, 905 new sonally identifiable information. Also, we had no access to accounts were activated. As a representative day, on June text of the messages exchanged or any other information 1 2006, there were almost 1 billion(982,005, 323)different that could be used to uniquely identify users. We focused on sessions(conversations among any number of people), with analyzing high-level characteristics and patterns that emerge ore than 7 billion IM messages sent. Approximately 9 from the collective dynamics of 240 million people, rather million users logged in with 64 million different users becom- alyzed data can be split into three parts: presence data, th s engaged in conversations on that day. Approximately 1.5 han the actions and characteristics of individuals. The an- illion new users that were not registered within Microsoft communication data, and user demographic information Messenger were invited to join on that particular day

cations, and then age. We found that homophily does not hold for gender; people tend to converse more frequently and with longer durations with the opposite gender. We also examined the relation between communication and dis￾tance, and found that the number of conversations tends to decrease with increasing geographical distance between con￾versants. However, communication links spanning longer distances tend to carry more and longer conversations. 2. INSTANT MESSAGING The use of IM has been become widely adopted in personal and businesss communications. IM clients allow users fast, near-synchronous communication, placing it between syn￾chronous communication mediums, such as real-time voice interactions, and asynchronous communication mediums like email [18]. IM users exchange short text messages with one or more users from their list of contacts, who have to be on￾line and logged into the IM system at the time of interaction. As conversations and messages exchanged within them are usually very short, it has been observed that users employ informal language, loose grammar, numerous abbreviations, with minimal punctuation [10]. Contact lists are commonly referred to as buddy lists and users on the lists are referred to as buddies. 2.1 Research on Instant Messaging Several studies on smaller datasets are related to this work. Avrahami and Hudson [3] explored communication characteristics of 16 IM users. Similarly, Shi et al. [13] ana￾lyzed IM contact lists submitted by users to a public website and explored a static contact network of 140,000 people. Re￾cently, Xiao et al. [20] investigated IM traffic characteristics within a large organization with 400 users of Messenger. Our study differs from the latter study in that we analyze the full Messenger population over a one month period, capturing the interaction of user demographic attributes, communica￾tion patterns, and network structure. 2.2 Data description To construct the Microsoft Instant Messenger communica￾tion dataset, we combined three different sources of data: (1) user demographic information, (2) time and user stamped events describing the presence of a particular user, and (3) communication session logs, where, for all participants, the number of exchanged messages and the periods of time spent participating in sessions is recorded. We use the terms session and conversation interchange￾ably to refer to an IM interaction among two or more people. Although the Messenger system limits the number of peo￾ple communicating at the same time to 20, people can enter and leave a conversation over time. We note that, for large sessions, people can come and go over time, so conversations can be long with many different people participating. We observed some very long sessions with more than 50 partic￾ipants joining over time. All of our data was anonymized; we had no access to per￾sonally identifiable information. Also, we had no access to text of the messages exchanged or any other information that could be used to uniquely identify users. We focused on analyzing high-level characteristics and patterns that emerge from the collective dynamics of 240 million people, rather than the actions and characteristics of individuals. The an￾alyzed data can be split into three parts: presence data, communication data, and user demographic information: 100 102 104 106 100 105 1010 γ = 3.6 number of Login events per user count Login every 20 minutes Login every 15 seconds 100 102 104 100 105 1010 γ = 2.2 number of AddBuddy events per user count (a) Login (b) AddBuddy Figure 1: Distribution of the number of events per user. (a) Number of logins per user. (b) Number of buddies added per user. • Presence events: These include login, logout, first ever login, add, remove and block a buddy, add un￾registered buddy (invite new user), change of status (busy, away, be-right-back, idle, etc.). Events are user and time stamped. • Communication: For each user participating in the session, the log contains the following tuple: session id, user id, time joined the session, time left the session, number of messages sent, number of messages received. • User data: For each user, the following self-reported information is stored: age, gender, location (country, ZIP), language, and IP address. We use the IP address to decode the geographical coordinates, which we then use to position users on the globe and to calculate dis￾tances. We gathered data for 30 days of June 2006. Each day yielded about 150 gigabytes of compressed text logs (4.5 terabytes in total). Copying the data to a dedicated eight￾processor server with 32 gigabytes of memory took 12 hours. Our log-parsing system employed a pipeline of four threads that parse the data in parallel, collapse the session join/leave events into sets of conversations, and save the data in a com￾pact compressed binary format. This process compressed the data down to 45 gigabytes per day. Processing the data took an additional 4 to 5 hours per day. A special challenge was to account for missing and dropped events, and session “id recycling” across different IM servers in a server farm. As part of this process, we closed a session 48 hours after the last leave session event. We closed sessions automatically if only one user was left in the conversation. 3. USAGE & POPULATION STATISTICS We shall first review several statistics drawn from aggre￾gations of users and their communication activities. 3.1 Levels of activity Over the observation period, 242,720,596 users logged into Messenger and 179,792,538 of these users were actively en￾gaged in conversations by sending or receiving at least one IM message. Over the month of observation, 17,510,905 new accounts were activated. As a representative day, on June 1 2006, there were almost 1 billion (982,005,323) different sessions (conversations among any number of people), with more than 7 billion IM messages sent. Approximately 93 million users logged in with 64 million different users becom￾ing engaged in conversations on that day. Approximately 1.5 million new users that were not registered within Microsoft Messenger were invited to join on that particular day

Female Male Figure 2: (a) Distribution of the number of people anticipating in a conversation.(b) Distribution of pread of du tions can be described by a power-law distribution. Figure 4: World and Messenger user population pyramid. Ages 15-30 are overrepresented in nger pop lation Figure 3:(a) Distribution of login duration. (b) Duration of times when people are not logged into the system(times between logout and login) Figure 5: Temporal characteristics of conversations We consider event distributions on a per-user basis in Fig (a) Average conversation duration per user;(b)time ure 1. The number of logins per user, displayed in Fig- etween conversations of users re 1(a), follows a heavy-tailed distribution with exponent 3.6. We note spikes in logins at 20 minute and 15 second atervals, which correspond to an auto-login function of the Focusing on the differences by gender, ger population es are overrep- resented for the 10-14 age interval. F 下m users. we see contact lists rather quickly. The spike at 600 buddies un- overall matches with the world population for age spans 10- doubtedly reflects the maximal allowed length of contac 14 and 35U39: for women users, we see a match for ages in Figure 2(a)displays the number of users per session. In the span of 30-34. We note that 6.5% of the population did Iessenger, multiple people can participate in conversations. not submit an age when creating their Messenger accounts people who can participate simultaneously in a conversa- 4. COMMUNICATION CHARACTERISTICS tion. Figure 2(b) shows the distribution over the session We now focus on characteristics and patterns durations, which can be modeled by a power-law distribu- munications. We limit the analysis to conversations between tion with exponent 3.6. two participants, which account for 99% of all conversations Next, we examine the distribution of the durations of pe. We first examine the distributions over conversation du- riods of time when people are logged on to the system. Let rations and times between conversations. Let user u have (tij, toj) denote a time ordered (tij< toj< tij+1)sequence C conversations in the observation period. Then, for every of online and offline times of a user, where ti, is the time conversation i of user u we create a tuple(tsu, i, teu, i, mu, i) where ts,: denotes the start time of the conversation, te Figure 3(a) plots the distribution of toj -tij over all j over is the end time of the conversation, and mu.i is the numbe users. Similarly, Figure 3(b) shows the distribution of of exchanged messages between the two users. We order the the periods of time when users are logged off, i.e. tij+1-to, conversations by their start time(tsu, i tsu, i +1).Then, over all j and over all Fitting the data to power-law calculate the aver distributions reveals exponents of 1.77 and 1.3, respectively. ration d(u)=2 teu, i-tsu, i, where the sum goes over The data shows that durations of being online tend to be all the u's conversations Figure 5(a) shows the distribution shorter and decay faster than durations that users are of of d(u) over all the users u. We find that the conversation fine. We also notice periodic effects of login durations of length can be described by a heavy-tailed distribution with 12, 24, and 48 hours, reflecting daily periodicities. We ob- exponent-3.7 and a mode of 4 minutes. serve similar periodicities for logout durations at multiples Figure 5(b)shows the intervals between consecutive con- of 24 hours 3.2 Demographic characteristics of the users tsu. i, where tsu. i+1 and tsu. i denote start times of two con- secutive conversations of user u. The power-law exponent of We compared the demographic characteristics of the Mes. the distribution over intervals is -1.5. This result is sim- senger population with 2005 world census data and found ilar to the temporal distribution for other kinds of human fferences between the statistics for age and gender. The communication activities, e.g., waiting times of emails and visualization of this comparison displayed in Figure 4 shows letters before a reply is generated 4. The exponent can be that users with reported ages in the 15-35 span of years are explained by a priority-queue model where tasks of different

100 101 102 103 104 105 106 107 108 109 100 101 102 Count Number of users per session ∝ x-3.5 20 102 103 104 105 106 107 108 109 1010 1011 100 101 102 Count Conversation duration ∝ x-3.67 Figure 2: (a) Distribution of the number of people participating in a conversation. (b) Distribution of the durations of conversations. The spread of dura￾tions can be described by a power-law distribution. 100 101 102 102 103 104 105 106 login duration count Data = 9.7e5 x−1.77 R2 =1.00 100 101 102 103 104 105 106 logout duration count Data = 6.9e5 x−1.34 R2 =1.00 Figure 3: (a) Distribution of login duration. (b) Duration of times when people are not logged into the system (times between logout and login). We consider event distributions on a per-user basis in Fig￾ure 1. The number of logins per user, displayed in Fig￾ure 1(a), follows a heavy-tailed distribution with exponent 3.6. We note spikes in logins at 20 minute and 15 second intervals, which correspond to an auto-login function of the IM client. As shown in Figure 1(b), many users fill up their contact lists rather quickly. The spike at 600 buddies un￾doubtedly reflects the maximal allowed length of contact lists. Figure 2(a) displays the number of users per session. In Messenger, multiple people can participate in conversations. We observe a peak at 20 users, the limit on the number of people who can participate simultaneously in a conversa￾tion. Figure 2(b) shows the distribution over the session durations, which can be modeled by a power-law distribu￾tion with exponent 3.6. Next, we examine the distribution of the durations of pe￾riods of time when people are logged on to the system. Let (tij , toj ) denote a time ordered (tij < toj < tij+1) sequence of online and offline times of a user, where tij is the time of the jth login, and toj is the corresponding logout time. Figure 3(a) plots the distribution of toj − tij over all j over all users. Similarly, Figure 3(b) shows the distribution of the periods of time when users are logged off, i.e. tij+1 −toj over all j and over all users. Fitting the data to power-law distributions reveals exponents of 1.77 and 1.3, respectively. The data shows that durations of being online tend to be shorter and decay faster than durations that users are of- fline. We also notice periodic effects of login durations of 12, 24, and 48 hours, reflecting daily periodicities. We ob￾serve similar periodicities for logout durations at multiples of 24 hours. 3.2 Demographic characteristics of the users We compared the demographic characteristics of the Mes￾senger population with 2005 world census data and found differences between the statistics for age and gender. The visualization of this comparison displayed in Figure 4 shows that users with reported ages in the 15–35 span of years are 0.1 0.05 0 0.05 0.1 0−4 5−9 10−14 15−19 20−24 25−29 30−34 35−39 40−44 45−49 50−54 55−59 60−64 65−69 70−74 75−79 80−84 85−89 90−94 95−99 100+ Female Male proportion of the population age World population MSN population Figure 4: World and Messenger user population age pyramid. Ages 15–30 are overrepresented in the Messenger population. 100 102 104 100 105 1010 conversation duration [min] count Data = 1.5e11 x−3.70 R2 =0.99 100 105 104 106 108 time between conversations [min] count Data = 3.9e9 x−1.53 R2 =0.99 1 day 2 days 3 days Figure 5: Temporal characteristics of conversations. (a) Average conversation duration per user; (b) time between conversations of users. strongly overrepresented in the active Messenger population. Focusing on the differences by gender, females are overrep￾resented for the 10–14 age interval. For male users, we see overall matches with the world population for age spans 10– 14 and 35U39; for women users, we see a match for ages in ˚ the span of 30–34. We note that 6.5% of the population did not submit an age when creating their Messenger accounts. 4. COMMUNICATION CHARACTERISTICS We now focus on characteristics and patterns with com￾munications. We limit the analysis to conversations between two participants, which account for 99% of all conversations. We first examine the distributions over conversation du￾rations and times between conversations. Let user u have C conversations in the observation period. Then, for every conversation i of user u we create a tuple (tsu,i, teu,i, mu,i), where tsu,i denotes the start time of the conversation, teu,i is the end time of the conversation, and mu,i is the number of exchanged messages between the two users. We order the conversations by their start time (tsu,i < tsu,i+1). Then, for every user u, we calculate the average conversation du￾ration d¯(u) = 1 C P i teu,i − tsu,i, where the sum goes over all the u’s conversations. Figure 5(a) shows the distribution of ¯d(u) over all the users u. We find that the conversation length can be described by a heavy-tailed distribution with exponent -3.7 and a mode of 4 minutes. Figure 5(b) shows the intervals between consecutive con￾versations of a user. We plot the distribution of tsu,i+1 − tsu,i, where tsu,i+1 and tsu,i denote start times of two con￾secutive conversations of user u. The power-law exponent of the distribution over intervals is − 1.5. This result is sim￾ilar to the temporal distribution for other kinds of human communication activities, e.g., waiting times of emails and letters before a reply is generated [4]. The exponent can be explained by a priority-queue model where tasks of different

1336|37 277301|277 213499 1251.42 (a)Number of conversations()Conversation duration 1.431 1.4 two-person conversations during June 2006. (a) Percentage of conversations among users of differ- ength in seconds umber of exchanged messages per conversation;(d) number of exchanged messages (c) Messages per conversation (d) Messages per unit time per minute of conversation Figure 6: Communication characteristics of users by reported age. We plot age vs. age and the color(z- serve a similar phenomenon when plotting the average num- axis )represents the intensity of communication ber of exchanged that fica. mi, displayed in Figure 6(c). Again, we find lder people exchange more messages, and we observe priorities arrive and wait until all tasks with higher priority a dip for ages 25-45 and a slight peak for ages 15-25. Fig- e addressed. This model generates a task waiting time ure 6(d)displays the number of exchanged messages per un distribution described by a power-law with exponent -1.5. time; for each age pair, (a, 6), we measure cao 2ieca. Here, we see that younger people have faster-paced dialogs 5. COMMUNICATION DEMOGRAPHICS while older people exchange messages at a slower Next we examine the interplay of communication and user We note that the younger population (ages 10-35 )are demographic attributes, i. e, how geography, location, age strongly biased towards communicating with people of a and gender influence observed communication patterns similar age(diagonal trend in Figure 6(a)), and that users who report being of ages 35 years and above tend to com- 5.1 Communication by age municate more evenly across ages(rectangular pattern in We sought to understand how communication among peo- Fig. 6(a)). Moreover, older people have conversations of the ple changes with the reported ages of participating users longest durations, with a"valley"in the duration of conver Figures 6(a)-(d)use a heat-map visualization to commu- sations for users of ages 25-35. Such a dip may represent nicate properties for different age-age pairs. The rows and shorter, faster-paced and more intensive conversations asso- columns represent the ages of both parties participating, and ciated with work-related communications. versus more ex- the color at each age-age cell captures the logarithm of the tended, slower, and longer interactions associated with social value for the pairing. The color spectrum extends from blue Discours low value) through green, yellow, and onto red(the highest value). Because of potential misreporting at very low and 5.2 Communication by gender high ages, we concentrate on users with self-reported ages that fall bet ween 10 and 60 years s We report on analyses of properties of pairwise communi cations as a function of the self-reported gender of users in Let a tuple(ai, bi, di, mi)denote the ith conversation conversations in Table 1. Let Cg, h=I(gi, hi, di, mi): gi the entire dataset that occurred among users of ages ai g Ahi= h denote a set of conversations where the two par and bi. The conversation had a duration of di seconds ticipating users are of genders g and h. Note that g takes 3 ring which mi messages were exchanged. Let Ca, b= possible values: female, male, and unknown(unreported) I(ai, bi, di, mi): ai= aA bi= b denote a set of all con- Table 1(a)relays Cg, h for combinations of genders g and versations between users of ages a and b, respectively. h. The table shows that approximately 50% of conversations Figure 6(a)shows the number of conversations among peo. occur between male and female and 40% of the conversations ple of different ages. For every pair of ages(a, b) the color occur among users of the same gender(20% for each).A indicates the size of set Ca.b. i.e., the number of different small number of conversations occur between people who conversations between users of ages a and b. We note that id not reveal their gender s the notion of a conversation is symmetric, the plots ar Similarly, Table 1(b)shows the average conversation length symmetric. Most conversations occur between people of ages seconds, broken down by the gender of conversant, com- 10 to 20. The diagonal trend indicates that people tend to puted as TCoh Ziece n di. We find that male-male conver alk to people of similar age. This is true especially for age sations tend to be shortest, lasting approximately 4 min- groups between 10 and 30 years. We shall explore this ob- utes. Female-female conversations last 4.5 minutes on the servation in more detail in Section 6 rsations have the longest du- Figure 6(b)displays a heat map for the average conver- rations, taking more than 5 minutes on average. Beyond sation duration, computed as We note aking place over longer periods of time, more messages are that older people tend to have longer conversations. We ob exchanged in female-male conversations. Table 1(c) lists

10 20 30 40 50 60 10 15 20 25 30 35 40 45 50 55 60 10 20 30 40 50 60 10 15 20 25 30 35 40 45 50 55 60 (a) Number of conversations (b) Conversation duration 10 20 30 40 50 60 10 15 20 25 30 35 40 45 50 55 60 10 20 30 40 50 60 10 15 20 25 30 35 40 45 50 55 60 (c) Messages per conversation (d) Messages per unit time Figure 6: Communication characteristics of users by reported age. We plot age vs. age and the color (z￾axis) represents the intensity of communication. priorities arrive and wait until all tasks with higher priority are addressed. This model generates a task waiting time distribution described by a power-law with exponent −1.5. 5. COMMUNICATION DEMOGRAPHICS Next we examine the interplay of communication and user demographic attributes, i.e., how geography, location, age, and gender influence observed communication patterns. 5.1 Communication by age We sought to understand how communication among peo￾ple changes with the reported ages of participating users. Figures 6(a)-(d) use a heat-map visualization to commu￾nicate properties for different age–age pairs. The rows and columns represent the ages of both parties participating, and the color at each age–age cell captures the logarithm of the value for the pairing. The color spectrum extends from blue (low value) through green, yellow, and onto red (the highest value). Because of potential misreporting at very low and high ages, we concentrate on users with self-reported ages that fall between 10 and 60 years. Let a tuple (ai, bi, di, mi) denote the ith conversation in the entire dataset that occurred among users of ages ai and bi. The conversation had a duration of di seconds during which mi messages were exchanged. Let Ca,b = {(ai, bi, di, mi) : ai = a ∧ bi = b} denote a set of all con￾versations between users of ages a and b, respectively. Figure 6(a) shows the number of conversations among peo￾ple of different ages. For every pair of ages (a, b) the color indicates the size of set Ca,b, i.e., the number of different conversations between users of ages a and b. We note that, as the notion of a conversation is symmetric, the plots are symmetric. Most conversations occur between people of ages 10 to 20. The diagonal trend indicates that people tend to talk to people of similar age. This is true especially for age groups between 10 and 30 years. We shall explore this ob￾servation in more detail in Section 6. Figure 6(b) displays a heat map for the average conver￾sation duration, computed as 1 |Ca,b| P i∈Ca,b di. We note that older people tend to have longer conversations. We ob- (a) U F M U 1.3 3.6 3.7 F 21.3 49.9 M 20.2 (b) U F M U 277 301 277 F 275 304 M 252 (c) U F M U 5.7 7.1 6.7 F 6.6 7.6 M 5.9 (d) U F M U 1.25 1.42 1.38 F 1.43 1.50 M 1.42 Table 1: Cross-gender communication, based on all two-person conversations during June 2006. (a) Percentage of conversations among users of differ￾ent self-reported gender; (b) average conversation length in seconds; (c) number of exchanged messages per conversation; (d) number of exchanged messages per minute of conversation. serve a similar phenomenon when plotting the average num￾ber of exchanged messages per conversation, computed as 1 |Ca,b| P i∈Ca,b mi, displayed in Figure 6(c). Again, we find that older people exchange more messages, and we observe a dip for ages 25–45 and a slight peak for ages 15–25. Fig￾ure 6(d) displays the number of exchanged messages per unit time; for each age pair, (a, b), we measure 1 |Ca,b| P i∈Ca,b mi di . Here, we see that younger people have faster-paced dialogs, while older people exchange messages at a slower pace. We note that the younger population (ages 10–35) are strongly biased towards communicating with people of a similar age (diagonal trend in Figure 6(a)), and that users who report being of ages 35 years and above tend to com￾municate more evenly across ages (rectangular pattern in Fig. 6(a)). Moreover, older people have conversations of the longest durations, with a “valley” in the duration of conver￾sations for users of ages 25–35. Such a dip may represent shorter, faster-paced and more intensive conversations asso￾ciated with work-related communications, versus more ex￾tended, slower, and longer interactions associated with social discourse. 5.2 Communication by gender We report on analyses of properties of pairwise communi￾cations as a function of the self-reported gender of users in conversations in Table 1. Let Cg,h = {(gi, hi, di, mi) : gi = g ∧hi = h} denote a set of conversations where the two par￾ticipating users are of genders g and h. Note that g takes 3 possible values: female, male, and unknown (unreported). Table 1(a) relays |Cg,h| for combinations of genders g and h. The table shows that approximately 50% of conversations occur between male and female and 40% of the conversations occur among users of the same gender (20% for each). A small number of conversations occur between people who did not reveal their gender. Similarly, Table 1(b) shows the average conversation length in seconds, broken down by the gender of conversant, com￾puted as 1 |Cg,h| P i∈Cg,h di. We find that male–male conver￾sations tend to be shortest, lasting approximately 4 min￾utes. Female–female conversations last 4.5 minutes on the average. Female–male conversations have the longest du￾rations, taking more than 5 minutes on average. Beyond taking place over longer periods of time, more messages are exchanged in female–male conversations. Table 1(c) lists

values for iCo.a zinco. mi and shows that, in female-male conversations, 7.6 messages are exchanged per conversation on the average as opposed to 6.6 and 5.9 for female-female and male-male, respectively. Table 1(d)shows the cor munication intensity computed as ∑icna:The number of messages exchanged per minute of conversation for male-female conversations is higher at 1.5 messages per ninute than for cross gender conversations, where the rate is 1.43 messages per minute. We examined the number of communication ties. where a tie is established between two people when they exchange at least one message during the observation period. We Figure 7: Number of users at a particular geographic female ties, and 640 million cross-gender ties. The Mes- location. Color of dots represents the number of senger population consists of 100 million males and 80 mil lion females by self report. These findings demonstrate that ties are not heavily gender biased; based on the popula tion, random chance predicts 31% male-male, 20% female- female, and 49% female-male links. We observe 25% male- male, 21% female-female, and 54% cross-gender links, thus demonstrating a minor bias of female-male links. The results reported in Table 1 run counter to prior stud ies reporting that communication among individuals who resemble one other(same gender) occurs more often(see 9 and references therein). We identified significant heterophily where people tend to communicate more with people of the pposite gender. However, we note that link heterogeneity was very close to the population value[8, i. e,, the number of same-and cross-gender ties roughly corresponds to randor Figure 8: Number of Messenger users per capita. chance. This shows there is no significant bias in linking Color intensity corresponds to the number of users for gender. However, we observe that cross-gender con per capita in the cell of the grid sations tend to be longer and to include more messages suggesting that more effort is devoted to conversations with Figure 9 shows a heat map that represents the intensi- the opposite sex. ties of Messenger communications on an international scale To create this map we place the world map on a fine grid 5.3 World geography and communicati where each cell of the grid contains the count of the number We now focus on the influence of geography and distance of conversations that pass through that point by increasing among participants on communications. Figure 7 shows the the count of all cells on the straight line between the geo- geographical locations of Messenger users. The general lo- locations of pairs of conversants. The color indicates the cation of the user was obtained via reverse IP lookup. We number of conversations crossing each point, providing a vi- plot all latitude/longitude positions linked to the position of sualization of the key flows of communication. For example, Australia and New Zealand have communications flowing dot corresponds to the logarithm of the number of logins towards Europe and United States. Similar flows hold for from the respective location, again using a spectrum of col- Japan. We see that Brazilian communications are weighted ors ranging from blue(low) through green and yellow to red toward Europe and Asia. We can also explore the flows of (high). Although the maps are built solely by plotting these transatlantic and US transcontinental communications positions, a recognizable world map is generated. We find that North America, Europe, and Japan are very dense, with 5.4 Communication among countries many users from those regions using Messenger. For the rest Communication among people within different countries of the world, the population of Messenger users appears so varies depending on the locations of conversants. We reside largely in coastal regions examine two such views. Figure 10(a) shows the top coun- We can condition the densities and behaviors of Messen- tries by the number of conversations between pairs of coun- ger users on multiple geographical and socioeconomic vari- tries. We examined all pairs of countries with more than ables and explore relationships between electronic commu 10 million conversations per month. The width of edges in nications and other attributes. As an example, harnessed the figure is proportional to the logarithm of the number of the United Nations gridded world population data to pro- conversations among the countries. We find that the United vide estimates of the number of people living in each cell. States and Spain appear to serve as hubs and that edges Given this data, and the data from Figure 7, we calculate appear largely between historically or ethnically connected the number of users per capita, displayed in Figure 8. Now countries. As examples, Spain is connected with the Span- we see transformed picture where several sparsely populated ish speaking countries in South America, Germany links to stand out as having a high usage per capita. These Turkey, Portugal to Brazil, and China to Korea. include the center of the United States, Canada. Figure 10(b) displays a similar plot where we consider navia. Ireland. Australia and South Korea. country pairs by the average duration of conversations. The

values for 1 |Cg,h| P i∈Cg,h mi and shows that, in female–male conversations, 7.6 messages are exchanged per conversation on the average as opposed to 6.6 and 5.9 for female–female and male–male, respectively. Table 1(d) shows the com￾munication intensity computed as 1 |Cg,h| P i∈Cg,h mi di . The number of messages exchanged per minute of conversation for male–female conversations is higher at 1.5 messages per minute than for cross-gender conversations, where the rate is 1.43 messages per minute. We examined the number of communication ties, where a tie is established between two people when they exchange at least one message during the observation period. We computed 300 million male–male ties, 255 million female– female ties, and 640 million cross-gender ties. The Mes￾senger population consists of 100 million males and 80 mil￾lion females by self report. These findings demonstrate that ties are not heavily gender biased; based on the popula￾tion, random chance predicts 31% male–male, 20% female– female, and 49% female–male links. We observe 25% male– male, 21% female–female, and 54% cross-gender links, thus demonstrating a minor bias of female–male links. The results reported in Table 1 run counter to prior stud￾ies reporting that communication among individuals who resemble one other (same gender) occurs more often (see [9] and references therein). We identified significant heterophily, where people tend to communicate more with people of the opposite gender. However, we note that link heterogeneity was very close to the population value [8], i.e., the number of same- and cross-gender ties roughly corresponds to random chance. This shows there is no significant bias in linking for gender. However, we observe that cross-gender conver￾sations tend to be longer and to include more messages, suggesting that more effort is devoted to conversations with the opposite sex. 5.3 World geography and communication We now focus on the influence of geography and distance among participants on communications. Figure 7 shows the geographical locations of Messenger users. The general lo￾cation of the user was obtained via reverse IP lookup. We plot all latitude/longitude positions linked to the position of servers where users log into the service. The color of each dot corresponds to the logarithm of the number of logins from the respective location, again using a spectrum of col￾ors ranging from blue (low) through green and yellow to red (high). Although the maps are built solely by plotting these positions, a recognizable world map is generated. We find that North America, Europe, and Japan are very dense, with many users from those regions using Messenger. For the rest of the world, the population of Messenger users appears to reside largely in coastal regions. We can condition the densities and behaviors of Messen￾ger users on multiple geographical and socioeconomic vari￾ables and explore relationships between electronic commu￾nications and other attributes. As an example, harnessed the United Nations gridded world population data to pro￾vide estimates of the number of people living in each cell. Given this data, and the data from Figure 7, we calculate the number of users per capita, displayed in Figure 8. Now we see transformed picture where several sparsely populated regions stand out as having a high usage per capita. These regions include the center of the United States, Canada, Scandinavia, Ireland, Australia, and South Korea. Figure 7: Number of users at a particular geographic location. Color of dots represents the number of users. Figure 8: Number of Messenger users per capita. Color intensity corresponds to the number of users per capita in the cell of the grid. Figure 9 shows a heat map that represents the intensi￾ties of Messenger communications on an international scale. To create this map, we place the world map on a fine grid, where each cell of the grid contains the count of the number of conversations that pass through that point by increasing the count of all cells on the straight line between the geo￾locations of pairs of conversants. The color indicates the number of conversations crossing each point, providing a vi￾sualization of the key flows of communication. For example, Australia and New Zealand have communications flowing towards Europe and United States. Similar flows hold for Japan. We see that Brazilian communications are weighted toward Europe and Asia. We can also explore the flows of transatlantic and US transcontinental communications. 5.4 Communication among countries Communication among people within different countries also varies depending on the locations of conversants. We examine two such views. Figure 10(a) shows the top coun￾tries by the number of conversations between pairs of coun￾tries. We examined all pairs of countries with more than 10 million conversations per month. The width of edges in the figure is proportional to the logarithm of the number of conversations among the countries. We find that the United States and Spain appear to serve as hubs and that edges appear largely between historically or ethnically connected countries. As examples, Spain is connected with the Span￾ish speaking countries in South America, Germany links to Turkey, Portugal to Brazil, and China to Korea. Figure 10(b) displays a similar plot where we consider country pairs by the average duration of conversations. The

(a)Number of conversations (b)Conversations per link Figure 1l: Communication with the distance Figure 9: A communication heat map. Correlation Probability AttributeRnd .00010.2970.0300 Gender0.0001-0.032‖0.4340.426 IP 00030.57‖0.0010.2 County0.00050.704‖0.0460.734 Language-0.00010.69410300.79s Table 2: Correlation coefficients and probability of users sharing an attribute for random pairs of people versus for pairs of people who communicate versation lengths do not increase with distance(see plots in 7). Conversation duration decreases with the distance, Figure 10: Communication among countries while the number of exchanged messages remains constant before decreasing slowly. Figure 11(b)shows the commu- (b)Countries by average length of the conversation. nications per link versus the distance among participant Edge widths correspond to logarithms of intensity The plot shows that longer links, i. e, connections between people who are farther apart, are more frequently used than shorter links. We interpret this finding to mean that peo- width of the edges are proportional to the mean length of communicate ple who are farther apart use Messenger more frequently to conversations between the countries. The core of the net work appears to be Arabic countries, including Saudi Ara- In summary, we observe that the total number of links and bia, Egypt, United Arab Emirates, Jordan, and Syria. associated conversations decreases with increasing distance conversations, the number of exchanged messages per con- 5.5 Communication and geographical distance versation, and the number of exchanged messages per unit We were interested in how communications change as the time. However, the number of times a link is used tends distance between people increases. We had hypothesized to increase with the distance among users. This suggests that the number of conversations would decrease with geo- that people who are farther apart tend to converse with IM graphical distance as users might be doing less coordination more frequently which perhaps takes the place of more ex- with one another on a daily basis, and where communication pensive long-distance voice telephony; voice might be used would likely require more effort to coordinate than might more frequently in lieu of IM for less expensive local com typically be needed for people situated more locally. We also conjectured that, once initiated, conversations among people who are farther apart would be somewhat longer as here might be a stronger need to catch up when the less- 6. HOMOPHILY OF COMMUNICATION frequent conversations occurred We performed several experiments to measure the level Figure 1l plots the relation between communication an at which people tend to communicate with similar people distance. Figure 11(a) shows the distribution of the nun First, we consider all 1.3 billion pairs of people who ex- ber of conversations between conversants at distance L. we changed at least one message in une 2006. and calculate found that the number of conversations decreases with dis- the similarity of various user demographic attributes. We tance. However, we observe a peak at a distance of appro contrast this with the similarity of pairs of users selected imately 500 kilometers. The other peaks and drops may re. via uniform random sampling across 180 million users. We eal geographical features. For example, a significant drop consider two measures of similarity: the correlation coeffi- n communication at distance of 5,000 km (3, 500 miles) may cient and the probability that users have the same attribute reflect the width of the atlantic ocean or the distance be. value, e.g., that users come from the same countries tween the east and west coasts of the United States. The Table 2 compares correlation coefficients of v number of links rapidly decreases with distance. This finding attributes when pairs of users are chosen uniformly at ran- suggests that users may use Messenger mainly for communi- dom with coefficients for pairs of users who communicate. cations with others within a local context and environment. We can see that attributes are not correlated for random We found that the number of exchanged messages and con- pairs of people, but that they are highly correlated for users

Figure 9: A communication heat map. Canada United States United Kingdom Venezuela Argentina Spain Taiwan China Hong Kong SAR Brazil Australia France Portugal Turkey Chile Dominican Republic Malaysia Peru Belgium Netherlands Mexico Egypt Colombia Thailand Germany Korea Morocco Saudi Arabia U.S.A. Egypt U.A.R U.K. Pakistan Oman Cameroon France Yugoslavia Croatia Syria Jordan Kuwait India Lebanon Netherlands Thailand Belgium Italy Poland Germany Palestinian Auth. Morocco Austria Bosnia Algeria Canada Israel Qatar Australia Sudan Azerbaijan Russia Bahrain Turkey Libya Yemen Iraq Figure 10: (a) Communication among countries with at least 10 million conversations in June 2006. (b) Countries by average length of the conversation. Edge widths correspond to logarithms of intensity of links. width of the edges are proportional to the mean length of conversations between the countries. The core of the net￾work appears to be Arabic countries, including Saudi Ara￾bia, Egypt, United Arab Emirates, Jordan, and Syria. 5.5 Communication and geographical distance We were interested in how communications change as the distance between people increases. We had hypothesized that the number of conversations would decrease with geo￾graphical distance as users might be doing less coordination with one another on a daily basis, and where communication would likely require more effort to coordinate than might typically be needed for people situated more locally. We also conjectured that, once initiated, conversations among people who are farther apart would be somewhat longer as there might be a stronger need to catch up when the less￾frequent conversations occurred. Figure 11 plots the relation between communication and distance. Figure 11(a) shows the distribution of the num￾ber of conversations between conversants at distance l. We found that the number of conversations decreases with dis￾tance. However, we observe a peak at a distance of approx￾imately 500 kilometers. The other peaks and drops may re￾veal geographical features. For example, a significant drop in communication at distance of 5,000 km (3,500 miles) may reflect the width of the Atlantic ocean or the distance be￾tween the east and west coasts of the United States. The number of links rapidly decreases with distance. This finding suggests that users may use Messenger mainly for communi￾cations with others within a local context and environment. We found that the number of exchanged messages and con- 0 0.5 1 1.5 2 x 104 1 2 3 4 5 6 x 107 distance [km] number of conversations Raw data Smooted 5000 10000 15000 6.5 6.6 6.7 6.8 6.9 7 7.1 7.2 distance [km] conversations per friendship Raw data Smooted (a) Number of conversations (b) Conversations per link Figure 11: Communication with the distance. Correlation Probability Attribute Rnd Comm Rnd Comm Age -0.0001 0.297 0.030 0.162 Gender 0.0001 -0.032 0.434 0.426 ZIP -0.0003 0.557 0.001 0.23 County 0.0005 0.704 0.046 0.734 Language -0.0001 0.694 0.030 0.798 Table 2: Correlation coefficients and probability of users sharing an attribute for random pairs of people versus for pairs of people who communicate. versation lengths do not increase with distance (see plots in [7]). Conversation duration decreases with the distance, while the number of exchanged messages remains constant before decreasing slowly. Figure 11(b) shows the commu￾nications per link versus the distance among participants. The plot shows that longer links, i.e., connections between people who are farther apart, are more frequently used than shorter links. We interpret this finding to mean that peo￾ple who are farther apart use Messenger more frequently to communicate. In summary, we observe that the total number of links and associated conversations decreases with increasing distance among participants. The same is true for the duration of conversations, the number of exchanged messages per con￾versation, and the number of exchanged messages per unit time. However, the number of times a link is used tends to increase with the distance among users. This suggests that people who are farther apart tend to converse with IM more frequently, which perhaps takes the place of more ex￾pensive long-distance voice telephony; voice might be used more frequently in lieu of IM for less expensive local com￾munications. 6. HOMOPHILY OF COMMUNICATION We performed several experiments to measure the level at which people tend to communicate with similar people. First, we consider all 1.3 billion pairs of people who ex￾changed at least one message in June 2006, and calculate the similarity of various user demographic attributes. We contrast this with the similarity of pairs of users selected via uniform random sampling across 180 million users. We consider two measures of similarity: the correlation coeffi- cient and the probability that users have the same attribute value, e.g., that users come from the same countries. Table 2 compares correlation coefficients of various user attributes when pairs of users are chosen uniformly at ran￾dom with coefficients for pairs of users who communicate. We can see that attributes are not correlated for random pairs of people, but that they are highly correlated for users

versation duration peaks at an age difference of 20 years between participants. We speculate that the peak may cor- respond roughly to the gap between generations The plots reveal that there is strong homophily in the com more with people of similar reported age. This is especially salient for the number of buddies and conversations among people of th ages. We also observe that the links between people of similar attributes are used more often, Figure 12: Numbers of pairs of people of different t with shorter and more intense(more exchanged ages.(a) Randomly selected pairs of people;(b)peo messages) communications. The intensity of communica- ple who communicate. Correlation between age and tion decays linearly with the difference in age. In contrast communication is captured by the diagonal trend to findings of previous studies, we observe that the num- ber of cross-gender communication links follows a random chance. However, cross-gender communication takes longer and is faster paced as it seems that people tend to pay more attention when communicating with the opposite sex. Recently, using the data we generated, Singla and Richard- son further investigated the homophily within the Messenger network and found that people who communicate are also more likely to search the web for content on similar top- (a)Number of conversations(b)Conversation duration ics[14 Figure 13: Communication characteristics and age 7. THE COMMUNICATION NETWORK difference between conversants So far we have examined communication patterns based on pairwise communications. We now create a more general communication network from the data. Using this network who communicate. As we noted earlier, gender and commu we can examine the typical social distance between people, nication are slightly negatively correlated; people tend to e, the number of links that separate a random pair of communicate more with people of the opposite gender people. This analysis seeks to understand how many peo- Another method for identifying association ple can be reached within certain numbers of hops among the probability that a pair of users will show an exact matc eople who communicate. Also, we test the transitivity of in values of an attribute, i. e, identifying whether two users the network, i. e, the degree at which pairs with a common come from the same country, speak the same language, etc friend tend to be connected Table 2 shows the results for the probability of users sharing We constructed a from the set of all two-user con- he same attribute value. We make similar observations as versations, where each node corresponds to a person and before. People who communicate are more likely to share there is an undirected edge between a pair of nodes if the common characteristics, including age, location, language, users were engaged in an active conversation during the ob- and they are less likely to be of the same gender. We note servation period (users exchanged at least 1 message). The that the most common attribute of people who com resulting network contains 179, 792, 538 nodes, and 1, 342, 246, 427 cate is language. On the flip side, the amount of commun edges. Note that this is not simply a buddy network; we ation tends to decrease with increasing user dissimilarity. only connect people who are buddies and have communi- This relationship is highlighted in Figure 11, which shows cated during the observation period how communication among pairs of people decreases with Figures 14-15 show the structural properties of the com- distance munication network. The network degree distribution shown Figure 12 further illustrates the results displayed in Ta- in Figure 14(a) is heavy tailed but does not follow a power ble 2, where we randomly sample pairs of users from the law distribution. Using maximum likelihood estimation, w messenger user base, and then plot the distribution over fit a power-law with exponential cutoff p(k)ok e with reported ages. As most of the population comes from the fitted parameter values a= 0.8 and b=0.03. We found a age group 10-30, the distribution of random pairs of people strong cutoff parameter and low power-law exponent, sug- reaches the mode at those ages but there is no correlation gesting a distribution with high variance igure 12(b)shows the distribution of ages over the pairs Figure 14(b) displays the degree distribution of a buddy of people who communicate. Note the correlation, as repre- graph. We did not have access to the full buddy network ented by the diagonal trend on the plot, where people tend we only had access to data on the length of the user contact to communicate more with others of a similar age list which allowed us to create the plot. We found a total Next, we further explore communication patterns by the of 9.1 billion buddy edges in the graph with 49 buddies per differences in the reported ages among users. Figure 13(a) user. We fit the data with a power-law distribution with plots on a log-linear scale the number of conversations in the. exponential cutoff and identified parameters of a=0.6 and social network with participants of varying age differences. b=0.01. The power-law exponent now is even smaller. Again we see that links and conversations are strongly cor- This model described the data well. We note a spike elated with the age differences among participants. Fig- 600 which is the limit on the maximal number of buddies ure 13(b) shows the average conversation duration with the imposed by the Messenger software client. The maximal age difference among the users. Interestingly, the mean con- number of buddies was increased to 300 from 150 in March

10 20 30 40 50 60 70 80 10 20 30 40 50 60 70 80 10 20 30 40 50 60 70 80 10 20 30 40 50 60 70 80 (a) Random (b) Communicate Figure 12: Numbers of pairs of people of different ages. (a) Randomly selected pairs of people; (b) peo￾ple who communicate. Correlation between age and communication is captured by the diagonal trend. 0 20 40 60 80 100 103 104 105 106 107 108 109 age difference number of conversations 0 20 40 60 80 4.4 4.6 4.8 5 5.2 5.4 age difference time per conversation [min] (a) Number of conversations (b) Conversation duration Figure 13: Communication characteristics and age difference between conversants. who communicate. As we noted earlier, gender and commu￾nication are slightly negatively correlated; people tend to communicate more with people of the opposite gender. Another method for identifying association is to measure the probability that a pair of users will show an exact match in values of an attribute, i.e., identifying whether two users come from the same country, speak the same language, etc. Table 2 shows the results for the probability of users sharing the same attribute value. We make similar observations as before. People who communicate are more likely to share common characteristics, including age, location, language, and they are less likely to be of the same gender. We note that the most common attribute of people who communi￾cate is language. On the flip side, the amount of communi￾cation tends to decrease with increasing user dissimilarity. This relationship is highlighted in Figure 11, which shows how communication among pairs of people decreases with distance. Figure 12 further illustrates the results displayed in Ta￾ble 2, where we randomly sample pairs of users from the Messenger user base, and then plot the distribution over reported ages. As most of the population comes from the age group 10–30, the distribution of random pairs of people reaches the mode at those ages but there is no correlation. Figure 12(b) shows the distribution of ages over the pairs of people who communicate. Note the correlation, as repre￾sented by the diagonal trend on the plot, where people tend to communicate more with others of a similar age. Next, we further explore communication patterns by the differences in the reported ages among users. Figure 13(a) plots on a log-linear scale the number of conversations in the social network with participants of varying age differences. Again we see that links and conversations are strongly cor￾related with the age differences among participants. Fig￾ure 13(b) shows the average conversation duration with the age difference among the users. Interestingly, the mean con￾versation duration peaks at an age difference of 20 years between participants. We speculate that the peak may cor￾respond roughly to the gap between generations. The plots reveal that there is strong homophily in the com￾munication network for age; people tend to communicate more with people of similar reported age. This is especially salient for the number of buddies and conversations among people of the same ages. We also observe that the links between people of similar attributes are used more often, to interact with shorter and more intense (more exchanged messages) communications. The intensity of communica￾tion decays linearly with the difference in age. In contrast to findings of previous studies, we observe that the num￾ber of cross-gender communication links follows a random chance. However, cross-gender communication takes longer and is faster paced as it seems that people tend to pay more attention when communicating with the opposite sex. Recently, using the data we generated, Singla and Richard￾son further investigated the homophily within the Messenger network and found that people who communicate are also more likely to search the web for content on similar top￾ics [14]. 7. THE COMMUNICATION NETWORK So far we have examined communication patterns based on pairwise communications. We now create a more general communication network from the data. Using this network, we can examine the typical social distance between people, i.e., the number of links that separate a random pair of people. This analysis seeks to understand how many peo￾ple can be reached within certain numbers of hops among people who communicate. Also, we test the transitivity of the network, i.e., the degree at which pairs with a common friend tend to be connected. We constructed a graph from the set of all two-user con￾versations, where each node corresponds to a person and there is an undirected edge between a pair of nodes if the users were engaged in an active conversation during the ob￾servation period (users exchanged at least 1 message). The resulting network contains 179,792,538 nodes, and 1,342,246,427 edges. Note that this is not simply a buddy network; we only connect people who are buddies and have communi￾cated during the observation period. Figures 14–15 show the structural properties of the com￾munication network. The network degree distribution shown in Figure 14(a) is heavy tailed but does not follow a power￾law distribution. Using maximum likelihood estimation, we fit a power-law with exponential cutoff p(k) ∝ k −a e −bk with fitted parameter values a = 0.8 and b = 0.03. We found a strong cutoff parameter and low power-law exponent, sug￾gesting a distribution with high variance. Figure 14(b) displays the degree distribution of a buddy graph. We did not have access to the full buddy network; we only had access to data on the length of the user contact list which allowed us to create the plot. We found a total of 9.1 billion buddy edges in the graph with 49 buddies per user. We fit the data with a power-law distribution with exponential cutoff and identified parameters of a = 0.6 and b = 0.01. The power-law exponent now is even smaller. This model described the data well. We note a spike at 600 which is the limit on the maximal number of buddies imposed by the Messenger software client. The maximal number of buddies was increased to 300 from 150 in March

10P L(Path length in hops) Core of order k (a)Communication b)k-cores Figure 14:(a) Degree distribution of communica- Figure 16:(a) Distribution over the shortest path tion network (number of people with whom a per- lengths. Average shortest path has length 6.6, the on communicates).(b)Degree distribution of the distribution reaches the mode at 6 hops, and the buddy network(length of the contact list) sizes of cores of order k s7.8;(b)distribution Figure 16(a)displays the distribution over the shortest path lengths. To approximate the distribution of the dis- tances, we randomly sampled 1000 nodes and calculated for d each node the shortest paths to all other nodes. We found k(Degree Weakly connected component that the distribution of path lengths reaches the mode at (a) Clustering (b)Components 6 hops and has a median at 7. The average path length is 6.6. This result means that a random pair of nodes in the Figure 15: (a) Clustering coefficient;(b)distribu Messenger network is 6.6 hops apart on the average, which is tion of connected components. 99.9% of the nodes half a link longer than the length measured by Travers and belong to the largest connected component milgram. The 90th percentile(effective diameter [16)of the distribution is 7. 8. 48% of nodes can be reached within 6 hops and 78% within 7 hops. So, we might say that, via the 2005, and was later raised to 600. With the data from June lens provided on the world by Messenger, we find that there 2006, we see only the peak at 600, and could not identify bumps at the earlier constraints. are about"7 degrees of separation"among people. We note Social networks have been found to be highly transitive that long paths, i. e, nodes that are far apart, exist in the e, people with common friends tend to be friends them- network; we found paths up to a length of 29 selves. The clustering coefficient [19 has been used as a measure of transitivity in the network. The measure is de- 7.2 Network cores fined as the fraction of triangles around a node of degre We further study connectivity of the communication net- k: [19. Figure 15(a) displays the clustering coefficient ver- work by examining the k-cores 5 of the graph. The concept sus the degree of a node for Messenger. Previous resul of k-core is a generalization of the giant connected compo- on measuring the web graph as well as theoretical analyses nent. The k-core of a network is a set of vertices K, where each vertex in K has at least k edges to other vertices in 1)with node degree k [ 11. For the Messenger network, K. The distribution of k-core sizes gives us an idea of how the clustering coefficient decays very slowly with exponent quickly the network shrinks as we move towards the cor 0.37 with the degree of a node and the average clustering The k-core of a graph can be obtained by deleting from coefficient is 0. 137. This result suggests that clustering in the network all vertices of degree less than k. This process the Messenger network is much higher than expected-that will decrease degrees of some non-deleted vertices, so more people with common friends also tend to be connected. Fig- vertices will have degree less than k. We keep pruning ver- ure 15(b)displays the distribution of the connected compo- tices until all remaining vertices have degree of at least k nents in the network. The giant component contains 99.9% We call the remaining vertices a k-core of the nodes in the network against a background of small Figure 16 plots the number of nodes in a core of order components, and the distribution follows a power law k. We note that the core sizes are remarkably stable up to 7.1 How small is the small world? a value of k N 20; the number of nodes in the core drops for only an order of magnitude. After k>20, the core us a unique opportunity to study size rapidly drops. The central part of the communication distances in the social network. To our knowledge, this is the network is composed of 79 nodes, where each of them has first time a planetary-scale social network has been available more than 68 edges inside the set. The structure of the o validate the well-known 6 degrees of separation"finding Messenger communication network is quite different from by Travers and Milgram [17. The earlier work employed the Internet graph; it has been observed [2 that the size of a sample of 64 people and found that the average number a k-core of the Internet decays as a power -law with k. Here of hops for a letter to travel from Nebraska to Boston was we see that the core sizes remains very stable up to a degre 6. 2(mode 5, median 5), which is popularly known as the 6 20, and only then start to rapidly degrease. This mean degrees of separation"among people. We used a population that the nodes with degrees of less than 20 are on the fringe mple that is more than two million times larger than the of the network, and that the core starts to rapidly decrease group studied earlier and confirmed the classic finding as nodes of degree 20 or more are deleted

10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 100 101 102 103 104 p(k) (probability) k (number of conversants) ∝ k-0.8 exp(-0.03⋅k) 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 101 102 103 p(b) (Probability) b (Number of buddies) ∝ b-0.6 exp(-0.01⋅b) (a) Communication (b) Buddies Figure 14: (a) Degree distribution of communica￾tion network (number of people with whom a per￾son communicates). (b) Degree distribution of the buddy network (length of the contact list). 10-3 10-2 10-1 100 101 102 c (Clustering coefficient) k (Degree) c ∝ k-0.37 100 101 102 103 104 105 106 107 100 101 102 103 104 105 106 107 108 109 Count Weakly connected component size largest component (99.9% of the nodes) (a) Clustering (b) Components Figure 15: (a) Clustering coefficient; (b) distribu￾tion of connected components. 99.9% of the nodes belong to the largest connected component. 2005, and was later raised to 600. With the data from June 2006, we see only the peak at 600, and could not identify bumps at the earlier constraints. Social networks have been found to be highly transitive, i.e., people with common friends tend to be friends them￾selves. The clustering coefficient [19] has been used as a measure of transitivity in the network. The measure is de- fined as the fraction of triangles around a node of degree k [19]. Figure 15(a) displays the clustering coefficient ver￾sus the degree of a node for Messenger. Previous results on measuring the web graph as well as theoretical analyses show that the clustering coefficient decays as k −1 (exponent −1) with node degree k [11]. For the Messenger network, the clustering coefficient decays very slowly with exponent −0.37 with the degree of a node and the average clustering coefficient is 0.137. This result suggests that clustering in the Messenger network is much higher than expected—that people with common friends also tend to be connected. Fig￾ure 15(b) displays the distribution of the connected compo￾nents in the network. The giant component contains 99.9% of the nodes in the network against a background of small components, and the distribution follows a power law. 7.1 How small is the small world? Messenger data gives us a unique opportunity to study distances in the social network. To our knowledge, this is the first time a planetary-scale social network has been available to validate the well-known “6 degrees of separation” finding by Travers and Milgram [17]. The earlier work employed a sample of 64 people and found that the average number of hops for a letter to travel from Nebraska to Boston was 6.2 (mode 5, median 5), which is popularly known as the “6 degrees of separation” among people. We used a population sample that is more than two million times larger than the group studied earlier and confirmed the classic finding. 10-12 10-10 10-8 10-6 10-4 10-2 100 0 5 10 15 20 25 30 p(l) (Probability) l, (Path length in hops) 101 102 103 104 105 106 107 108 109 100 101 102 Number of nodes Core of order K k=20 k=60-68, n=79 (a) Diameter (b) k-cores Figure 16: (a) Distribution over the shortest path lengths. Average shortest path has length 6.6, the distribution reaches the mode at 6 hops, and the 90% effective diameter is 7.8; (b) distribution of sizes of cores of order k. Figure 16(a) displays the distribution over the shortest path lengths. To approximate the distribution of the dis￾tances, we randomly sampled 1000 nodes and calculated for each node the shortest paths to all other nodes. We found that the distribution of path lengths reaches the mode at 6 hops and has a median at 7. The average path length is 6.6. This result means that a random pair of nodes in the Messenger network is 6.6 hops apart on the average, which is half a link longer than the length measured by Travers and Milgram. The 90th percentile (effective diameter [16]) of the distribution is 7.8. 48% of nodes can be reached within 6 hops and 78% within 7 hops. So, we might say that, via the lens provided on the world by Messenger, we find that there are about “7 degrees of separation” among people. We note that long paths, i.e., nodes that are far apart, exist in the network; we found paths up to a length of 29. 7.2 Network cores We further study connectivity of the communication net￾work by examining the k-cores [5] of the graph. The concept of k-core is a generalization of the giant connected compo￾nent. The k-core of a network is a set of vertices K, where each vertex in K has at least k edges to other vertices in K. The distribution of k-core sizes gives us an idea of how quickly the network shrinks as we move towards the core. The k-core of a graph can be obtained by deleting from the network all vertices of degree less than k. This process will decrease degrees of some non-deleted vertices, so more vertices will have degree less than k. We keep pruning ver￾tices until all remaining vertices have degree of at least k. We call the remaining vertices a k-core. Figure 16 plots the number of nodes in a core of order k. We note that the core sizes are remarkably stable up to a value of k ≈ 20; the number of nodes in the core drops for only an order of magnitude. After k > 20, the core size rapidly drops. The central part of the communication network is composed of 79 nodes, where each of them has more than 68 edges inside the set. The structure of the Messenger communication network is quite different from the Internet graph; it has been observed [2] that the size of a k-core of the Internet decays as a power-law with k. Here we see that the core sizes remains very stable up to a degree ≈ 20, and only then start to rapidly degrease. This means that the nodes with degrees of less than 20 are on the fringe of the network, and that the core starts to rapidly decrease as nodes of degree 20 or more are deleted

7.3 Strength of the ties It has been observed by Albert et al. 1 that many real world networks are robust to node-level changes or attacks Researchers have showed that networks like the World wide Web, Internet, and several social networks display a high degree of robustness to random node removals, i. e, one has o remove many nodes chosen uniformly at random to make the network disconnected. On the contrary, targeted attacks are very effective. Removing a few high degree nodes can have a dramatic influence on the connectivity of a network Let us now study how the Messenger communication net work is decomposed when"strong, "i. e, heavily used, edges are removed from the network We consider several different definitions of"heavily used, "and measure the types of edges ◆奢 that are most important for network connectivity. We note that a similar experiment was performed by Shi et al [13 Figure 17: Relative size of the largest connected in the context of a small Im buddy network. The author component as a function of number of nodes re- of the prior study took the number of common friends at moved the ends of an edge as a measure of the link strength. A the number of edges here is too large(1.3 billion)to remove edges one by one, we employed the following procedure: We order the nodes by decreasing value per a measure of the intensity of engagement of users; we then delete nodes as- sociated with users in order of decreasing measure and we bserve the evolution of the properties of the communication network as nodes are deleted We consider the following different measures of engage- -e- Avg sent Average sent: The average number of sent messages per users conversation Average time: The average duration of user's conver- 日= Random sations Links: The number of links of a user(node degree) i. e, number of different people he or she exchanged Figure 18: Number of removed edges as nodes are messages with deleted by order of different measures of engage- Conversations: The total number of conversations of a lel user in the observation period Sent messages: The total number of sent messages by time per conversation, average number of sent messages, or a user in the observation period number of sent messages per unit time. We were not sur- Sent per unit time: The number of sent messages per prised to find that the size of the largest component size de- unit time of a conversation creases most rapidly when nodes are deleted in order of the e Total time. The total conversation time of a user in decreasing number of links that they have, i. e the number the observation period of people with whom a user at a node communicates. Ran- dom ordering of the nodes shrinks the component at the At each step of the experiment, we remove 10 million slowest rate. After removing 160 million out of 180 million nodes in order of the specific measure of engagement being nodes with the random policy, the largest component still studied. We then determine the relative size of the largest contains about half of the nodes. Surprisingly, when deleting connected component, i. e, given the network at particu- p to 100 million nodes, the average time per conversation lar step, we find the fraction of the nodes belonging to th neasure shrinks the component even more slowly than the largest connected component of the network random deletion policy. Figure 17 plots the evolution of the fraction of nodes in Figure 18 displays plots of the number of removed edges the largest connected component with the number of deleted from the network as nodes are deleted. Similar to the rela- nodes. We plot a separate curve for each of the seven dif- tionships in Figure 17, we found that deleting nodes by the ferent measures of engagement. For comparison, we also inverse number of edges removes edges the fastest. As in consider the random deletion of the node Figure 18, the same group of node ordering criteria(num- The decomposition procedure highlighted two types of dy ber of conversations, total conversation time or number of namics of network change with node removal. The size of the sent messages)removes edges from the networks as fast as largest component decreases rapidly when we use the number of links criteria. However, we find that ran- sures of engagement the number of links, number of conver dom node removal removes edges in a linear manner. Edges sations, total conversation time, or number of sent messages. re removed at a lower rate when deleting nodes by aver- In contrast, the size of the largest component decreases very age time per conversation, average numbers of sent mes- slowly when we use as a measure of engagement the average sages, or numbers of sent messages per unit time. We be-

7.3 Strength of the ties It has been observed by Albert et al. [1] that many real￾world networks are robust to node-level changes or attacks. Researchers have showed that networks like the World Wide Web, Internet, and several social networks display a high degree of robustness to random node removals, i.e., one has to remove many nodes chosen uniformly at random to make the network disconnected. On the contrary, targeted attacks are very effective. Removing a few high degree nodes can have a dramatic influence on the connectivity of a network. Let us now study how the Messenger communication net￾work is decomposed when “strong,” i.e., heavily used, edges are removed from the network. We consider several different definitions of “heavily used,” and measure the types of edges that are most important for network connectivity. We note that a similar experiment was performed by Shi et al [13] in the context of a small IM buddy network. The authors of the prior study took the number of common friends at the ends of an edge as a measure of the link strength. As the number of edges here is too large (1.3 billion) to remove edges one by one, we employed the following procedure: We order the nodes by decreasing value per a measure of the intensity of engagement of users; we then delete nodes as￾sociated with users in order of decreasing measure and we observe the evolution of the properties of the communication network as nodes are deleted. We consider the following different measures of engage￾ment: • Average sent: The average number of sent messages per user’s conversation • Average time: The average duration of user’s conver￾sations • Links: The number of links of a user (node degree), i.e., number of different people he or she exchanged messages with • Conversations: The total number of conversations of a user in the observation period • Sent messages: The total number of sent messages by a user in the observation period • Sent per unit time: The number of sent messages per unit time of a conversation • Total time: The total conversation time of a user in the observation period At each step of the experiment, we remove 10 million nodes in order of the specific measure of engagement being studied. We then determine the relative size of the largest connected component, i.e., given the network at particu￾lar step, we find the fraction of the nodes belonging to the largest connected component of the network. Figure 17 plots the evolution of the fraction of nodes in the largest connected component with the number of deleted nodes. We plot a separate curve for each of the seven dif￾ferent measures of engagement. For comparison, we also consider the random deletion of the nodes. The decomposition procedure highlighted two types of dy￾namics of network change with node removal. The size of the largest component decreases rapidly when we use as mea￾sures of engagement the number of links, number of conver￾sations, total conversation time, or number of sent messages. In contrast, the size of the largest component decreases very slowly when we use as a measure of engagement the average 0 2 4 6 8 10 12 14 16 x 107 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Deleted nodes Component size Avg. sent Avg. time Links Conversations Sent messages Sent per unit time Total time Random Figure 17: Relative size of the largest connected component as a function of number of nodes re￾moved. 0 2 4 6 8 10 12 14 16 x 107 0 2 4 6 8 10 12 14 x 108 Deleted nodes Deleted edges Avg. sent Avg. time Links Conversations Sent messages Sent per unit time Total time Random Figure 18: Number of removed edges as nodes are deleted by order of different measures of engage￾ment. time per conversation, average number of sent messages, or number of sent messages per unit time. We were not sur￾prised to find that the size of the largest component size de￾creases most rapidly when nodes are deleted in order of the decreasing number of links that they have, i.e., the number of people with whom a user at a node communicates. Ran￾dom ordering of the nodes shrinks the component at the slowest rate. After removing 160 million out of 180 million nodes with the random policy, the largest component still contains about half of the nodes. Surprisingly, when deleting up to 100 million nodes, the average time per conversation measure shrinks the component even more slowly than the random deletion policy. Figure 18 displays plots of the number of removed edges from the network as nodes are deleted. Similar to the rela￾tionships in Figure 17, we found that deleting nodes by the inverse number of edges removes edges the fastest. As in Figure 18, the same group of node ordering criteria (num￾ber of conversations, total conversation time or number of sent messages) removes edges from the networks as fast as the number of links criteria. However, we find that ran￾dom node removal removes edges in a linear manner. Edges are removed at a lower rate when deleting nodes by aver￾age time per conversation, average numbers of sent mes￾sages, or numbers of sent messages per unit time. We be-

lieve that these findings demonstrate that users with long e hope that our studies with Messenger data serves a onversations and many messages per conversation tend to an example of directions in social science research, highlight have smaller degrees-even given the findings displayed in ing how communication systems can provide insights about Figure 17, where we saw that removing these users is more high-level patterns and relationships in human communica- effective for breaking the connectivity of the network than tions without making incursions into the privacy of individ- for random node deletion. Figure 18 also shows that using uals. We hope that this first effort to understand a social the average number of messages per conversation as a crite- network on a genuinely planetary scale will embolden others rion removes edges in the slowest manner. We believe that to explore human behavior at large scales this makes sense intuitively If users invest similar amounts Acknowledgments of time to interacting with others, then people with short We thank Dan Liebling for help with generated world map conversations will tend to converse with more people given amount of time than users having long conversations. plots, and Dimitris Achlioptas and Susan Dumais for helpful uggestion 8. CONCLUSION 9.R RENCES 1 R. Albert, H. Jeong, and A.-L. Barabasi. Error and We have reviewed a set of results eration and analysis of an anonymize the communication patterns of all 2J. I. Alvarez-Hamelin, L. Dall'Asta, A. Barrat, and IM system. The methods and findi A. Vespignani. Analysis and visualization of large scale using a large IM network as a worldwide lens onto aggregate Systems, 2005 human behavior 图3] We described the creation of the dataset, capturing high- characteristics of instant messaging: effects and level communication activities and demographics in June predictions of interpersonal relationships. In Cscw 2006. The core dataset contains more than 30 billion conver. 4A origin of bursts and heavy tails in sations among 240 million people. We discussed the creation and analysis of a communication graph from the data con- 5 V aining 180 million nodes and 1.3 billion edges. The commu S/0202039).Feb200 nication network is largest social network analyzed to date et Analysis. Worldwide Enterprise In Messaging Applications 2005-2009 Forecast and The planetary-scale network allowed us to explore dependen the Decks for Substantial cies among user demographics, communication characteris- Growth. 2005 tics, and network structure. Working with such a massive 7 J. Leskovec and E. Horvitz. Worldwide Buzz: dataset allowed us to test hypotheses such as the average chain of separation among people across the entire world. ech. report MSR-TR-2006-186, 2006 of americans We discovered that the graph is well connected, highly ] transitive. and robust. We reviewed the influence of multi- . M. Co ple factors on communication frequency and duration. We Birds of a feather: Homophily in social networks. found strong influences of homophily in activities, where nnual Review of Sociology, 27(1): 415-444, 2001 people with similar characteristics tend to communicate more, I de. bradney with the exception of gender, where we found that cross- action In CSCW 00: Proceedings of the AcM gender conversations are both more frequent and of longer upported cooperative work, duration than conversations with users of the same reported gender. We also examined the path lengths and validated [11]E. Ravasz an of planetary scale earlier research that found 6 degree eparat 12E312201m%是E We note that the sheer size of the data limits the kinds Homophily-heterophily: Relational concepts for of analyses one can perform. In some cases, a smaller ran- communication research. Public Opinion Quarterly, dom sample may avoid the challenges with working with [13]X Shi, L.A.Adamic, and M.J.Strauss. Networks of corrupt the structural properties of networks, such as the de- ree distribution and the diameter of the graphs [15]. Thus, [141 hile sampling may be valuable for managing complexity social networks to personal behavior of analyses, results on network properties with partial data WWv8.2008 sets may be rendered unreliable. Furthermore. we need to [15 M. P Stumpf, C Wiuf, R. M. May. Subnets of consider the full data set to reliably measure the patterns of ge and distance homophily in communication (16) 5.pperties of networks. PNAS, 102(22d 2003 In other directions of research with the dataset. we have tual model for the internet topol pursued the use of machine learning and inference to learn [171 J. Travers and s. Milgram. An exper munication frequencies and durations of conversation nong [18 A. Voida, W. C. Newstetter, and E.D. Mynatt.When people as a function of the structural and demographic at- conventions collide: the tensions of instant messaging tributes of ersants.Our future directions for research (19 Dt. J. watts and s H. strogatz Colective dynamics of include gaining an understanding of the dynamics of the tructure of the communication network via a study of the 20 evolution of the network over time essaging traffic characteristics. In ICDCS 07, 200

lieve that these findings demonstrate that users with long conversations and many messages per conversation tend to have smaller degrees—even given the findings displayed in Figure 17, where we saw that removing these users is more effective for breaking the connectivity of the network than for random node deletion. Figure 18 also shows that using the average number of messages per conversation as a crite￾rion removes edges in the slowest manner. We believe that this makes sense intuitively: If users invest similar amounts of time to interacting with others, then people with short conversations will tend to converse with more people in a given amount of time than users having long conversations. 8. CONCLUSION We have reviewed a set of results stemming from the gen￾eration and analysis of an anonymized dataset representing the communication patterns of all people using a popular IM system. The methods and findings highlight the value of using a large IM network as a worldwide lens onto aggregate human behavior. We described the creation of the dataset, capturing high￾level communication activities and demographics in June 2006. The core dataset contains more than 30 billion conver￾sations among 240 million people. We discussed the creation and analysis of a communication graph from the data con￾taining 180 million nodes and 1.3 billion edges. The commu￾nication network is largest social network analyzed to date. The planetary-scale network allowed us to explore dependen￾cies among user demographics, communication characteris￾tics, and network structure. Working with such a massive dataset allowed us to test hypotheses such as the average chain of separation among people across the entire world. We discovered that the graph is well connected, highly transitive, and robust. We reviewed the influence of multi￾ple factors on communication frequency and duration. We found strong influences of homophily in activities, where people with similar characteristics tend to communicate more, with the exception of gender, where we found that cross￾gender conversations are both more frequent and of longer duration than conversations with users of the same reported gender. We also examined the path lengths and validated on a planetary scale earlier research that found “6 degrees of separation” among people. We note that the sheer size of the data limits the kinds of analyses one can perform. In some cases, a smaller ran￾dom sample may avoid the challenges with working with terabytes of data. However, it is known that sampling can corrupt the structural properties of networks, such as the de￾gree distribution and the diameter of the graphs [15]. Thus, while sampling may be valuable for managing complexity of analyses, results on network properties with partial data sets may be rendered unreliable. Furthermore, we need to consider the full data set to reliably measure the patterns of age and distance homophily in communications. In other directions of research with the dataset, we have pursued the use of machine learning and inference to learn predictive models that can forecast such properties as com￾munication frequencies and durations of conversations among people as a function of the structural and demographic at￾tributes of conversants. Our future directions for research include gaining an understanding of the dynamics of the structure of the communication network via a study of the evolution of the network over time. We hope that our studies with Messenger data serves as an example of directions in social science research, highlight￾ing how communication systems can provide insights about high-level patterns and relationships in human communica￾tions without making incursions into the privacy of individ￾uals. We hope that this first effort to understand a social network on a genuinely planetary scale will embolden others to explore human behavior at large scales. Acknowledgments We thank Dan Liebling for help with generated world map plots, and Dimitris Achlioptas and Susan Dumais for helpful suggestions. 9. REFERENCES [1] R. Albert, H. Jeong, and A.-L. Barabasi. Error and attack tolerance of complex networks. Nature, 406:378, 2000. [2] J. I. Alvarez-Hamelin, L. Dall’Asta, A. Barrat, and A. Vespignani. Analysis and visualization of large scale networks using the k-core decomposition. In ECCS ’05: European Conference on Complex Systems, 2005. [3] D. Avrahami and S. E. Hudson. Communication characteristics of instant messaging: effects and predictions of interpersonal relationships. In CSCW ’06, pages 505–514, 2006. [4] A.-L. Barabasi. The origin of bursts and heavy tails in human dynamics. Nature, 435:207, 2005. [5] V. Batagelj and M. Zaversnik. Generalized cores. ArXiv, (cs.DS/0202039), Feb 2002. [6] IDC Market Analysis. Worldwide Enterprise Instant Messaging Applications 2005–2009 Forecast and 2004 Vendor Shares: Clearing the Decks for Substantial Growth. 2005. [7] J. Leskovec and E. Horvitz. Worldwide Buzz: Planetary-Scale Views on an Instant-Messaging Network. Tech. report MSR-TR-2006-186, 2006. [8] P. V. Marsden. Core discussion networks of americans. American Sociological Review, 52(1):122–131, 1987. [9] M. McPherson, L. Smith-Lovin, and J. M. Cook. Birds of a feather: Homophily in social networks. Annual Review of Sociology, 27(1):415–444, 2001. [10] B. A. Nardi, S. Whittaker, and E. Bradner. Interaction and outeraction: instant messaging in action. In CSCW ’00: Proceedings of the 2000 ACM conference on Computer supported cooperative work, pages 79–88, 2000. [11] E. Ravasz and A.-L. Barabasi. Hierarchical organization in complex networks. Physical Review E, 67(2):026112, 2003. [12] E. M. Rogers and D. K. Bhowmik. Homophily-heterophily: Relational concepts for communication research. Public Opinion Quarterly, 34:523–538, 1970. [13] X. Shi, L. A. Adamic, and M. J. Strauss. Networks of strong ties. Physica A Statistical Mechanics and its Applications, 378:33–47, May 2007. [14] P. Singla and M. Richardson. Yes, there is a correlation - from social networks to personal behavior on the web. In WWW ’08, 2008. [15] M. P. Stumpf, C. Wiuf, R. M. May. Subnets of scale-free networks are not scale-free: sampling properties of networks. PNAS, 102(12), 2005. [16] S. L. Tauro, C. Palmer, G. Siganos, and M. Faloutsos. A simple conceptual model for the internet topology. In GLOBECOM ’01, vol. 3, pages 1667 – 1671, 2001. [17] J. Travers and S. Milgram. An experimental study of the small world problem. Sociometry, 32(4), 1969. [18] A. Voida, W. C. Newstetter, and E. D. Mynatt. When conventions collide: the tensions of instant messaging attributed. In CHI ’02, pages 187–194, 2002. [19] D. J. Watts and S. H. Strogatz. Collective dynamics of ’small-world’ networks. Nature, 393:440–442, 1998. [20] Z. Xiao, L. Guo, and J. Tracey. Understanding instant messaging traffic characteristics. In ICDCS ’07, 2007