B. Ordering clustering coefficient of node V. The density is calculated as The ordering procedure consists on the measurement of the the real size of edges where the origin and destiny nodes are coefficients and their normalization by using an adjustment in C divided by the quantity of edges of the clique( complete mechanism. It is not different from a regular ordering graph)formed by all the nodes contained in C mechanism, since it also use only one numeric value related to each node to be ordered. The indexing value belonging to ∑ Ec ojec(M1)) ach node is a result of a process that measures the (C|*(C|-1)/2 nteraction strength between that node and the central node of the entire recommendation process The measurement of this interaction is chosen as the result where Mi is the element ij of the adjacency matrix of a weighted average among three independent indexes. 1) First Index These indexes measure specific properties of a sub-graph he first index is defined as the number of adjacent nodes omposed by the nodes that are analyzed. Three indicators that are linked at the same time to node i and node j, where i are analyzed in this present article. However other index can is the center node of the analysis and j is the node that is still be used to improve the precision of the weighting values. These metrics were used because of its simplicity being ordered for the recommendation system. So, we have and the intuitive ideas of how friend should be connected In the literature of complex networks several metrics to evaluate the strength of interaction between two nodes were h1i=C:n presented[4, [8], [9]. We choose the friend-of-friends In a social networks this index measures the quantity of one of the three measurements. Inspired by the concept of common mends between person i and person J lustering coefficient, we also applied two other metrics. 2) Second index Both of them measure the clustering of a set of nodes that The second index refers to the density of the result links the two nodes in question. The referred nodes are the measured by the first index recommended node. Those measures are chosen b the simplicity and linkage connection between the its possible recommended friend This index measures the cohesion level inside the " small group formed by the common friends of person i and person B If this index has a small value then the people inside this group are not well-related. Figure 4 shows a sub-graph representing common friends between tw his connected friends and friend-of-friends i ocial network. The can be spit in two different regions. The re er and his friends. Region B represents friend Fig. 4. Sub-graph of the relationship from white and black vertex. The Some variable and concept are defined to derive the regio %diacent vertexes important for both users are shown in the circled friends of the main user dexes used for the friend recommendation system. First we define Ci as the set of the nodes adjacent to node vi and Dc 3 )Third Index are defined as the adjacency density among the node The third index is a variation of the second. This index contained in the C set. This measure is inspired in the measures the density of the group formed by the adjacent clustering coefficient definition, whereas Dc is the vertices of node n and node n Instead of an intersection.B. Ordering The ordering procedure consists on the measurement of the coefficients and their normalization by using an adjustment mechanism. It is not different from a regular ordering mechanism, since it also use only one numeric value related to each node to be ordered. The indexing value belonging to each node is a result of a process that measures the interaction strength between that node and the central node of the entire recommendation process. The measurement of this interaction is chosen as the result of a weighted average among three independent indexes. These indexes measure specific properties of a sub-graph composed by the nodes that are analyzed. Three indicators are analyzed in this present article. However other index can still be used to improve the precision of the weighting values. These metrics were used because of its simplicity and the intuitive ideas of how friend should be connected. In the literature of complex networks several metrics to evaluate the strength of interaction between two nodes were presented [4], [8], [9]. We choose the friend-of-friends (FOF) concept, which is a simple and widely used idea as one of the three measurements. Inspired by the concept of clustering coefficient, we also applied two other metrics. Both of them measure the clustering of a set of nodes that links the two nodes in question. The referred nodes are the node that will receive the recommendation and the possible recommended node. Those measures are chosen based on the simplicity and linkage connection between the user and its possible recommended friend. Fig. 3. A visual example of a sub-network showing the links between single users in relation to his connected friends and friend-of-friends in a social network. The network can be spit in two different regions. The region A represents the central user and his friends. Region B represents friends of friends of the main user. Some variable and concept are defined to derive the indexes used for the friend recommendation system. First we define C as the set of the nodes adjacent to node v and D are defined as the adjacency density among the node contained in the C set. This measure is inspired in the clustering coefficient definition, whereas  is the clustering coefficient of node v . The density is calculated as the real size of edges where the origin and destiny nodes are in C divided by the quantity of edges of the clique (complete graph) formed by all the nodes contained in C.  = ∑∈(∑∈( )) (|| ∗ (|| − 1))⁄2 where  is the element ij of the adjacency matrix. 1) First Index The first index is defined as the number of adjacent nodes, that are linked at the same time to node i and node j, where i is the center node of the analysis and j is the node that is being ordered for the recommendation system. So, we have:  =  ∩   In a social networks this index measures the quantity of common friends between person i and person j. 2) Second Index The second index refers to the density of the result measured by the first index:  =  ∩ This index measures the cohesion level inside the “small” group formed by the common friends of person i and person j. If this index has a small value then the people inside this group are not well-related. Figure 4 shows a sub-graph representing common friends between two users, ni and nj . Fig. 4. Sub-graph of the relationship from white and black vertex. The common adjacent vertexes important for both users are shown in the circled region. 3) Third Index The third index is a variation of the second. This index measures the density of the group formed by the adjacent vertices of node ni and node nj . Instead of an intersection, 235