Game theory, Extremal optimization, and Community Structure Detection in Complex Networks

The network community detection problem consists in identifying groups of nodes that are more densely connected to each other than to the rest of the network. The lack of a formal definition for the notion of community led to the design of various solution concepts and computational approaches to this problem, among which those based on optimization and, more recently, on game theory, received a special attention from the heuristic community. The former ones define the community structure as an optimum value of a fitness function, while the latter as a game equilibrium. Both are appealing as they allowed the design and use of various heuristics. This paper analyses the behavior of such a heuristic that is based on extremal optimization, when used either as an optimizer or within a game theoretic setting. Numerical results, while significantly better than those provided by other state-of-art methods, for some networks show that differences between tested scenarios do not indicate any superior behavior when using game theoretic concepts; moreover, those obtained without using any selection for survival suggest that the search is actually guided by the inner mechanism of the extremal optimization method and by the fitness function used to evaluate and compare components within an individual.