Spread of Information in a Social Network Using Influential Nodes

Spread of Information in a

Social Network Using

Influential Nodes

Arpan Chaudhury

Partha Basuchowdhuri

Subhashis Majumder

(Heritage Institute of

Technology, Kolkata)

Introduction A social network is a set of actors

that may have relationships with one another.

It can be further described as the graph of relationships and interactions between a set of individuals.

Nodes are the individuals (visitors) within the networks, and ties are the different types of relationships between the individuals.

Social Networks

In a social network

represents a node

or a person

represents an edge

or a relationship

Our Aim

To find the set

of the most

“influential” such

that we can

maximize the

spread of

information

through those

“influentials”

Where to use….

-Viral marketing

-Word-of-mouth

marketing

strategies

Strategies to stop-

-Telecom churn

-Disease spread

Motivation behind our approach

- lesser the degree

of a node, the

correlation plot

shows that if we

choose that node as

that node as the

only seed to start

the spread of

information in the

network, more the

# of hops it takes

Why MST (Max. Spanning Tree) ?

Path through which information is more likely to flow

Identify nodes with high spread potential

Identify bridges passing information from one group to another

Remove insignificant edges retaining all nodes

0

4

2

1

5

6

7

3

8

3.5

2.5

4.5

3

44

4.5

3.54

2.5

2.53

3.5

D(0)=4D(1)=1

D(2)=2

D(3)=5D(4)=3

D(7)=3

D(5)=3

D(6)=4

D(8)=1

w(x) denotes weight of an edge x.

c(x) denotes cost of an edge x.

0.4

0.33

0.250.22

Max. Spanning Tree of the Network

Weight of the EdgesDegree of the NodesA Network

Edges in maximum spanning tree of the network represent the most

probable path of information flow

0.25

0.25

0.4

0.22

Modifying the graph to build MST

)(

1)(

2

)()()(

ij

ij

ij

eweC

jDiDew

Information Flow Path

Influential

Node

Information

Flow Path

Algorithm – Part I

Algorithm – Part II

Experimental Results

Dolphin Network

Dolphin network

with 62 vertices and

159 edges.

Popularly used as

benchmark data for

community

detection algorithms

in SNA.

Dolphin Network

Maximum spanning

tree of dolphin

network.

Dolphin Network

Core of dolphin

network, with k=7

AS Relationship Network

AS relation network

with 6474 vertices

and 13895 edges

from CAIDA.

Used here to test

our algorithm for a

large dataset

Maximum spanning

tree (MST) of

AS relationship

network.

AS Relationship Network

Core of AS

relationship network,

with k=18 (dth=50)

AS Relationship Network

Greedy k-center Vs. core-finding

Green/ cyan – first hop, Yellow – second hop,

Blue – third hop, Pink – fourth hop, White – fifth hop

Comparative study

Hop by hop spread comparison

Hop by hop spread comparison

Conclusion

Efficient and accurate compared to k-center.

Spread is simplistic and not community based,

hence takes very less time.

Work has been updated based on degree

discount and the model has been generalized

according to independent cascade model (all

edges won’t lead to spread).

Thank You