There only one group, which does not tally with

There are many complex
systems that are collections of individual components linked in some way. Examples
include human societies and the Internet. To study such systems and their
properties, networks (or graphs) have been used to represent such complex
systems in the real world. In recent years, with increasing accessibility and
availability of data about various kinds of large systems, network analysis has
become an important topic.

 

Community
detection is one of the most interesting and complex topics in the field of
network studies because of its significant relations with the studies of criminology (BELLAIR, 1997), biology (Santo Fortunato, 2007), social marketing (McKenzie-Mohr, 2000), and many other disciplines.
For example, identifying customer communities in the social network could help
find the target market and improve the performance and efficiency when
determining marketing strategies. The detection of communities within networks refers
to the division of vertices into groups according to the edge pattern in the
network. Communities reveal the relationships between nodes and the internal
organization of the network (Andrea Lancichinetti, 2008). An overall and
comprehensive knowledge of the community structure might help us get better acquainted
with the network organization.

We Will Write a Custom Essay Specifically
For You For Only $13.90/page!


order now

 

Many
algorithms for community detection have been devised and proposed in recent
years, however, most of them assume that communities are disjoint, i.e., each
vertex belongs to only one group, which does not tally with situations in the
real world. For example, a student might join both football club and tennis club.
In this case, the two clubs partially overlap with each other. Motivated from
this, the project focuses on devising a game theoretic algorithm for detecting
overlapping communities based on the trial
and error model (Bei, Chen, Dou, Huang, & Qiang, 2013).

 

1.1.      
Assumptions

Our
model assumes that each individual makes rational choice to adopt a new
strategy if the utility (

)
would increase, otherwise, the individual would keep his prior strategy. Beyond
that, each vertex is a single community at the initial state.