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Social Networks Extended Fuzzy Adjacency Matrix Outlines Introduction Social Networks Adjacency Matrix Fuzzy Adjacency Matrix Our Work Extended Fuzzy Adjacency Matrix Facebook App Future Work Social Networks What is Social Network? Social Networks A social structure which represents interdependency of Individuals SNA SNA(Social Network Analysis): Analyzing the relationships between social objects (people and groups…) by representing them as edges and nodes. A main tool in SNA is Adjacency Matrix. Adjacency Matrix Nodes: X = {x1 x2 … xn} Relationships: matrix R Two values (0 & 1) are not able to describe intensities of relationships. Adjacency matrix R is a poor representation of relationships. x1 x2 x3 x1 1 0 1 x2 0 1 1 x3 1 1 1 Fuzzy Adjacency Matrix: Fuzzy Set Classical Set: i.e. an element either belongs or does not belong to the set. Fuzzy set: A generalization of classical set. Introducing membership function M(x,y) to indicate the Membership Grade, which is the degree to how much a member x belongs to a set y. i.e. 0<M(x,y)<1: x is to a certain degree belonging to y Fuzzy Adjacency Matrix We define relationships R as a membership function R(xi,xj). Fuzzy adjacency matrix shows intensities of relationships. R(xi,xj) = R(xj,xi) ? x1 x2 x3 x1 1 0.6 0.8 x2 0.6 1 0.3 x3 0.8 0.3 1 Our Work A new model for social network Extended Fuzzy Adjacency Matrix An algorithm for calculating relationships An app based on our model Facebook Relationship App Extended Fuzzy Adjacency Matrix Bidirectional? Symmetrical? Extended Fuzzy Adjacency Matrix Alice 0.9 0.1 Bob John 0.9 0.5 0.5 0 0.9 0 0.2 0 David Eric Extended Fuzzy Adjacency Matrix x1 x2 x3 X1 R11 R12 R13 x2 R21 R22 R23 x3 R31 R32 R33 Algorithm C F A H E D B G Algorithm FA={C, D, E} FB={C, D, F, G, H} Sort F’A={C, E, D} F’B={C, F, H, D, G} Algorithm R(A,B) = (3/4 + 1/4)*2/3 = 2/3 R(B,A) = (5/6 + 2/6)*2/5 = 7/15 Algorithm For unconnected nodes X and Y: 1 Check available paths, if no, R(X,Y)= 0; 2 For all the paths, calculate: 3 Check if there is any path “XSTY” such that R(X,S) > k, R(S,T) > k, R(T,Y) > k; if yes back to step 2, if no, output k . Algorithm Based App Calculating relationships according to: Number of Alice and Bob’s mutual friends; Number of Alice’s comments on Bob’s wall; Self definition. Alice Bob Alice App Structure Facebook Server User UserInfo App Server Third Party App Ranked and calculated Info Application Finding jobs My VIPs Schedule …… Future Work Properties of EFAM(Extended Fuzzy Adjacency Matrix) Leaning ability Experiments