The weight combination solution is obtained by appl second condition focuses on the users most likely to respond 70 selected user. it w the genetic algorithm. Using this combination the initial set to the experiment. For each of of candidate is ordered to produce the recommendation list. generated a set of 10 recommendations, among which 20% The filtering step can reduce the set of candidate based on using the FOF algorithm. However, before sending the the first index, avoiding measuring the second and third recommended list of friends to the recipients, we still have to index for less relevant nodes. The indexes evaluated from replace those that were already part of their friends list nodes ny to n] are the same as n2 to ni, so reducing by half relationships. This step conveys the first result. We call it the the time needed for the solution for the entire network This does not mean that if n2 is recommended for nI, nI will be correct set of one-way relationships. Our proposed solution presents a rate of 20.83% while the FOF algorithm achieved recommended for n2, since each user has his own context 13.33%. Note that the low value for this rate does not imply with singular weight combination. In a applied situation, the bad results since a person can link to another person recommendation can be previously generated, and the without having a common interest. These are common cases weight combination could be preserved for the user for a of celebrity user such as movie actors. In the twitter site the period of time and them recalculated, depending on increase best connect person does not necessary is connected to all of the friend network list of the user the users that are connected to him. After this procedure, the IV. EXPERIMENTS recommendations are sent in the form of links to the profile of users recommended and instructions to accept or reject Usually experiments to validate solutions in machine the recommendation. After a period of 10 days, 31 of 70 learning uses well established data sets. This data are users used the recommendations. It was counted only the normally divided in training, validation and test set which acceptance of recommendation without the need of the re prepared specifically for the purpose of evaluating the recommended user to have done the reverse action. Using performance of the algorithm used to solve the problem. The our algorithm 77.69% of the recommendations were procedures enable the comp of different solutions accepted while the FOF algorithm achieved 72.22% success led from different method applied in the same data ship recommendation in TABLE I social networks does not have a straightforward method to EXPERIMENTAL RESULTS validate the results since the objective is to generate a list of GBFRGA FOF recommendation that is dependable on the user Complex networks have been shown to be a promising 20.83% 13,33% area for research in recent years. Several problems can be Acceptance of the modeled in network structures. Despite all the progress, commendation 77,69% 72,22% recommendation in complex networks has been a problem poorly explored. A validation technique to assess the quality of the proposed algorithm would be necessary to compare V. CONCLUSION AND FUTURE WORKS the recommended list of relationships, to a certain user, wit the desired objective. For privacy reasons social networks We have presented a friend recommendation system based normlly do not provide or give access to information on the topology of a social network. The knowledge of the necessary to perform this experiments. Most of the times. structure and topology of these SNSs combined with each SNSs develops their own methods and algorithms for quantitative properties of the graph are used to develop the recommendation but the limited access to this method make recommendation system. The social network used, the Oro- it difficult a cross-validation. A direct consequence of this Aro, is smaller than the most of the popular social networks, fact is that there is no public data set prepared for such as Facebook, Orkut or Myspace. Besides being smaller experiments on the recommendation of relationships in size. it is also less accessed. hence the rate of 44% of user social networks response to the experiment. As expected, our algorithm was To solve the problem of lack of a common public data, w better than the fof another solution that is also based obtained through C.E. S.A. R the data of their social network, etwork topology. Despite the small difference between the Oro-Aro to test the proposed method. The experiment performances, we believe that the size and dynamics of the consisted of analyzing the algorithm being used by network plays role. The Oro-Aro network has only selected group of users. For each user we present a list of 634 users, and the average of the friend per users is only 8.1 recommendations of new relationships. Then, we evaluated Thus, we can assume that the FOF algorithm performs well in small networks; however the resulting list is probably used the algorithm FOF (friend-of-friend) for a subset of the small. In larger networks, like Facebook or Orkut in which users. Of the 655 users of the Oro-Aro 70 were selected. the average friend size exceeds 200, the FOF could not They satisfy the condition of having at least 13 relationships distinguish the best recommendations when there are small and have accessed the network in the last 45 days. The first differences in FOF criteria. The reason why our solution can condition is necessary because the algorithm uses the perform better in larger networks is because of its hybrid topology, making sure that the subnet of each user with a ature of taking in consideration three different indexes. himum size is relevant and that it display a pattern. The Since the FOF is used as part of our solution which implic 238The weight combination solution is obtained by applying the genetic algorithm. Using this combination the initial set of candidate is ordered to produce the recommendation list. The filtering step can reduce the set of candidate based on the first index, avoiding measuring the second and third index for less relevant nodes. The indexes evaluated from nodes n1 to n2 are the same as n2 to n1, so reducing by half the time needed for the solution for the entire network. This does not mean that if n2 is recommended for n1, n1 will be recommended for n2, since each user has his own context with singular weight combination. In a applied situation, the recommendation can be previously generated, and the weight combination could be preserved for the user for a period of time and them recalculated, depending on increase of the friend network list of the user. IV. EXPERIMENTS Usually experiments to validate solutions in machine learning uses well established data sets. This data are normally divided in training, validation and test set which are prepared specifically for the purpose of evaluating the performance of the algorithm used to solve the problem. The procedures enable the comparison of different solutions obtained from different method applied in the same data set. However, the problem of relationship recommendation in social networks does not have a straightforward method to validate the results since the objective is to generate a list of recommendation that is dependable on the user. Complex networks have been shown to be a promising area for research in recent years. Several problems can be modeled in network structures. Despite all the progress, recommendation in complex networks has been a problem poorly explored. A validation technique to assess the quality of the proposed algorithm would be necessary to compare the recommended list of relationships, to a certain user, with the desired objective. For privacy reasons social networks normally do not provide or give access to information necessary to perform this experiments. Most of the times, each SNSs develops their own methods and algorithms for recommendation but the limited access to this method make it difficult a cross-validation. A direct consequence of this fact is that there is no public data set prepared for experiments on the recommendation of relationships in social networks. To solve the problem of lack of a common public data, we obtained through C.E.S.A.R the data of their social network, Oro-Aro to test the proposed method. The experiment consisted of analyzing the algorithm being used by a selected group of users. For each user we present a list of recommendations of new relationships. Then, we evaluated the acceptance of the recommendations. For comparison, we used the algorithm FOF (friend-of-friend) for a subset of the users. Of the 655 users of the Oro-Aro 70 were selected. They satisfy the condition of having at least 13 relationships and have accessed the network in the last 45 days. The first condition is necessary because the algorithm uses the topology, making sure that the subnet of each user with a minimum size is relevant and that it display a pattern. The second condition focuses on the users most likely to respond to the experiment. For each of the 70 selected user, it was generated a set of 10 recommendations, among which 20% using the FOF algorithm. However, before sending the recommended list of friends to the recipients, we still have to replace those that were already part of their friends list before the pre-processing network, i.e., the one-way relationships. This step conveys the first result. We call it the correct set of one-way relationships. Our proposed solution presents a rate of 20.83% while the FOF algorithm achieved 13.33%. Note that the low value for this rate does not imply a bad results since a person can link to another person without having a common interest. These are common cases of celebrity user such as movie actors. In the twitter site the best connect person does not necessary is connected to all the users that are connected to him. After this procedure, the recommendations are sent in the form of links to the profile of users recommended and instructions to accept or reject the recommendation. After a period of 10 days, 31 of 70 users used the recommendations. It was counted only the acceptance of recommendation without the need of the recommended user to have done the reverse action. Using our algorithm 77.69% of the recommendations were accepted while the FOF algorithm achieved 72.22% success. TABLE II EXPERIMENTAL RESULTS GBFRGA FOF correct set of one-way relationships 20,83% 13,33% Acceptance of the recommendation 77,69% 72,22% V. CONCLUSION AND FUTURE WORKS We have presented a friend recommendation system based on the topology of a social network. The knowledge of the structure and topology of these SNSs combined with quantitative properties of the graph are used to develop the recommendation system. The social network used, the Oro￾Aro, is smaller than the most of the popular social networks, such as Facebook, Orkut or Myspace. Besides being smaller in size, it is also less accessed, hence the rate of 44% of user response to the experiment. As expected, our algorithm was better than the FOF, another solution that is also based on network topology. Despite the small difference between the performances, we believe that the size and dynamics of the network plays a major role. The Oro-Aro network has only 634 users, and the average of the friend per users is only 8.1. Thus, we can assume that the FOF algorithm performs well in small networks; however the resulting list is probably small. In larger networks, like Facebook or Orkut in which the average friend size exceeds 200, the FOF could not distinguish the best recommendations when there are small differences in FOF criteria. The reason why our solution can perform better in larger networks is because of its hybrid nature of taking in consideration three different indexes. Since the FOF is used as part of our solution which implies 238