About nash equilibrium, modularity optimization, and network community structure detection

Abstract

The concept of community in complex networks, which is intuitively expressed as a group of nodes more densely connected to each other than to the rest of the network, has not been formally defined yet in a manner that encompasses all aspect ensuing from this intuitive description. Among existing approaches, a popular one consists in considering the network community structure as the optimum value of a fitness function that reflects the modularity of the network. Recently, a new trend to model the problem as a game having the community structure as equilibrium has emerged. Both approaches are appealing as they allow the design of heuristic approaches to this problem and benefit from their adaptability and scalability. This paper analyzes the behavior of such a heuristic that is based on extremal optimization in combination with two possible game theoretic models that consider different payoff functions, in comparison with the corresponding optimization approaches.