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Social Networks Extended Fuzzy Adjacency Matrix

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.

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Social Networks Extended Fuzzy Adjacency Matrix

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  1. Social Networks Extended Fuzzy Adjacency Matrix

  2. Outlines • Introduction • Social Networks • Adjacency Matrix • Fuzzy Adjacency Matrix • Our Work • Extended Fuzzy Adjacency Matrix • FacebookApp • Future Work

  3. Social Networks • What is Social Network?

  4. Social Networks A social structure which represents interdependency of Individuals

  5. 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.

  6. Adjacency Matrix • Nodes: X = {x1 x2 … xn} • Relationships: matrix R x1 x2x3 x1 x2 x3 1 0 1 Problem!!! 0 1 1 • Two values (0 & 1) are not able to describe intensities of relationships. • Adjacency matrix R is a poor representation of relationships. 1 1 1

  7. 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

  8. Fuzzy Adjacency Matrix • We define relationships R as a membership function • R(xi,xj). x1 x2x3 x1 x2 x3 1 0.6 0.8 0.6 1 0.3 • Fuzzy adjacency matrix shows • intensities of relationships. 0.8 0.3 1 R(xi,xj) = R(xj,xi) ?

  9. Our Work • A new model for social network • Extended Fuzzy Adjacency Matrix • An algorithm for calculating relationships • An app based on our model • FacebookRelationship App

  10. Extended Fuzzy Adjacency Matrix Bidirectional? Symmetrical?

  11. Extended Fuzzy Adjacency Matrix Alice 0.9 Bob 0.1 John 0.9 0.9 0 0.5 0 0.5 0 0.2 David Eric

  12. Extended Fuzzy Adjacency Matrix x1 x2x3 R11 R12 R13 X1 x2 x3 R21 R22 R23 R31 R32 R33

  13. Algorithm C F A H E D B G

  14. Algorithm

  15. Algorithm • R(A,B) = (3/4 + 1/4)*2/3 = 2/3 • R(B,A)= (5/6 + 2/6)*2/5 = 7/15

  16. 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 .

  17. 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.

  18. App Structure Facebook Server User UserInfo App Server Third Party App Ranked and calculated Info

  19. Application • Finding jobs • My VIPs • Schedule • ……

  20. Future Work • Properties of EFAM(Extended Fuzzy Adjacency Matrix) • Leaning ability • Experiments

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