1. Social Networks Extended Fuzzy Adjacency Matrix

2. Outlines Introduction Social Networks Adjacency Matrix Fuzzy Adjacency Matrix Our Work Extended Fuzzy Adjacency Matrix Facebook App 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 = {x 1 x 2 … x n } Relationships: matrix R Problem!!! Two values (0 & 1) are not able to describe intensities of relationships. Adjacency matrix R is a poor representation of relationships. x 1 x 2 x 3 x1x2x3x1x2x3

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. 0<M(x,y)<1: x is to a certain degree belonging to y i.e.

8. Fuzzy Adjacency Matrix We define relationships R as a membership function R(x i,x j ). x 1 x 2 x 3 x1x2x3x1x2x3 Fuzzy adjacency matrix shows intensities of relationships. R(x i,x j ) = R(x j,x i ) ?

9. 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

10. Extended Fuzzy Adjacency Matrix Bidirectional? Symmetrical?

11. Extended Fuzzy Adjacency Matrix 0.9 0.1 0.5 0 0.2 0 0 0.9

12. Extended Fuzzy Adjacency Matrix x 1 x 2 x 3 X1x2x3X1x2x3

13. A C D E F G B H Algorithm

14. FA={C, D, E} F B ={C, D, F, G, H} F’A={C, E, D} F’ B ={C, F, H, D, G} Sort

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. AliceBob Alice

18. App Structure UserInfo Ranked and calculated Info

19. Application Finding jobs My VIPs Schedule ……

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