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Social Networks Extended Fuzzy Adjacency Matrix
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OutlinesIntroduction
Social NetworksAdjacency MatrixFuzzy Adjacency Matrix
Our WorkExtended Fuzzy Adjacency MatrixFacebook App
Future Work
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Social Networks
What is Social Network?
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Social NetworksA social structure which representsinterdependency of Individuals
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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.
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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
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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.
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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) ?
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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
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Extended Fuzzy Adjacency Matrix
Bidirectional?
Symmetrical?
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Extended Fuzzy Adjacency Matrix
Alice
DavidEric
BobJohn
0.9
0.1
0.50.5 0
0.2 00
0.90.9
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Extended Fuzzy Adjacency Matrix
R11 R12
R21 R22
R13
R23
R31 R32 R33
x1 x2 x3
X1
x2
x3
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A
C
D
E
F
GB
H
Algorithm
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Algorithm
FA={C, D, E}
FB={C, D, F, G, H}
F’A={C, E, D}
F’B={C, F, H, D, G}
Sort
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Algorithm
R(A,B) = (3/4 + 1/4)*2/3 = 2/3
R(B,A) = (5/6 + 2/6)*2/5 = 7/15
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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 .
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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
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App Structure
Facebook Server
App Server
User
Third Party App
Use
rInfo
Ranked and calculated Info
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Application
Finding jobs
My VIPs
Schedule
……
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Future Work
Properties of EFAM(Extended Fuzzy Adjacency Matrix)
Leaning ability
Experiments
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