Social Networks Extended Fuzzy Adjacency Matrix
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Transcript of Social Networks Extended Fuzzy Adjacency Matrix
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
SNASNA(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 SetClassical 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 MatrixWe 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 WorkA 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
Bob John
0.90.1
0.5 0.5 00.2 0
00.90.9
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 AppCalculating 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
Facebook Server
App Server
User
Third Party App
UserInfo
Ranked and calculated Info
ApplicationFinding jobs
My VIPs
Schedule
……
Future WorkProperties of EFAM(Extended Fuzzy Adjacency Matrix)
Leaning ability
Experiments