Social Networks Extended Fuzzy Adjacency Matrix

OutlinesIntroduction

Social NetworksAdjacency MatrixFuzzy Adjacency Matrix

Our WorkExtended Fuzzy Adjacency MatrixFacebook App

Future Work

Social Networks

What is Social Network?

Social NetworksA social structure which representsinterdependency 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 MatrixNodes: X = {x1 x2 … xn}

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.

1 0 1

0 1 1

x1 x2 x3

1 1 1

x1

x2

x3

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.

Fuzzy Adjacency Matrix

We define relationships R as a membership function

R(xi,xj).

1 0.6 0.8

0.6 1 0.3

x1 x2 x3

0.8 0.3 1

x1

x2

x3

Fuzzy adjacency matrix shows

intensities of relationships.R(xi,xj) = R(xj,xi) ?

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

DavidEric

BobJohn

0.9

0.1

0.50.5 0

0.2 00

0.90.9

Extended Fuzzy Adjacency Matrix

R11 R12

R21 R22

R13

R23

R31 R32 R33

x1 x2 x3

X1

x2

x3

A

C

D

E

F

GB

H

Algorithm

Algorithm

FA={C, D, E}

FB={C, D, F, G, H}

F’A={C, E, D}

F’B={C, F, H, D, G}

Sort

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 BobAlice

App Structure

Facebook Server

App Server

User

Third Party App

Use

rInfo

Ranked and calculated Info

Application

Finding jobs

My VIPs

Schedule

……

Future Work

Properties of EFAM(Extended Fuzzy Adjacency Matrix)

Leaning ability

Experiments