### Social Networks: Fuzzy Set

```Social Networks
Outlines
Introduction
Social Networks
Our Work
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.
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
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
We define relationships R as a membership function
R(xi,xj).
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
An algorithm for calculating relationships
An app based on our model
Bidirectional?
Symmetrical?
Alice
0.9
0.1
Bob
John
0.9
0.5
0.5
0
0.9
0
0.2
0
David
Eric
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
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
```