Article | REF: H7444 V1

Detection community

Authors: Michel CRAMPES, Michel PLANTIÉ

Publication date: May 10, 2014

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ABSTRACT

The growing interest on social networks on the Internet highlights the problem of community detection. The objective is to gather together individuals according to criteria which make them look similar whilst distinguishing the resulting groups as much as possible. The most frequent methods are presented, with more details on those which use intrinsic properties of the analyzed networks, such as modularity. To compute in reasonable time these methods produce only approximated results. These results can be improved to obtain stable communities according to a Nash Equilibrium.

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AUTHORS

  • Michel CRAMPES: LGI2P Laboratory - École des Mines d'Alès, Nîmes site

  • Michel PLANTIÉ: LGI2P Laboratory - École des Mines d'Alès, Nîmes site

 INTRODUCTION

From the village to the soccer club, from the family to school alumni associations, from the workplace to groups of individuals sharing the same passion, men and women have many opportunities to forge ties of varying strength, whether occasional or permanent. These ties can be territorialized when they are built around events that have a physical and temporal reality (birth, schooling, work, trade fairs, etc.). They can also be dematerialized when they stem from shared cultures or social practices. The Internet has opened up new forms of dematerialized social links. Social networks have become a new field of investigation, much sought-after by both research and industry. Their formal translation can be found in graphs.

However, social bonds generally function through the emergence of groups. For example, a wedding provides an opportunity to bring together a family group, and often also a group of friends. In practice, social ties lead to community ties. More than a social being, who fits into a fabric, man is a community being insofar as his membership of a community enriches him with the traits shared by the members of that community, and at the same time leads him to enrich the traits common to the members of the community.

Happy or unhappy dynamics result from this belonging, whether explicit or implicit. Armed conflicts, religious wars or even battles between rival suburban tribes are an unfortunate illustration of this. Conversely, communities, which are the result of social ties, in turn create social bonds, and encourage exchanges. The creation and life of communities is at once a social, cultural and economic fact. Studying them and helping to build them opens up a particularly rich new field of scientific and industrial research.

The detection of communities was initially a field of research initiated by sociologists. The analysis of issues is a difficult exercise, given their number and the extremely varied forms they take, some of which may be politically sensitive. At one extreme, the formation of sports teams, for example rugby teams, is not a problem in terms of the number of teams (the creation of a team is the political decision of a city or a sponsor) or the number of players (15 in a team for rugby à 15, 9 cyclists for the Tour de France). On the other hand, it still poses a problem in terms of team composition, a subject we'll address at the end of this article. There are also countless company cases where the stakes are high. For example, the justification of citizens' belonging to a locality, a region, or from a region to a country is a very evocative case.

For example, the simple criterion of the frequency of telephone exchanges

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KEYWORDS

community detection   |   overlaping communities   |   Nash equilibrium   |   sociology   |   statistics   |   data analysis   |   social networks


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