Evolutionary Detection of Community Structures in Complex Networks: a New Fitness Function

The discovery and analysis of communities in networks is a topic of high interest in sociology, biology and computer science. Complex networks in nature and society range from the immune system and the brain to social, communication and transport networks. The key issue in the development of algorithms able to automatically detect communities in complex networks refers to a meaningful quality evaluation of a community structure. Given a certain grouping of nodes into communities, a good measure is needed to evaluate the quality of the community structure based on the definition that a strong community has dense intra-connections and sparse outside-community links. We propose a new fitness function for the assessment of community structures quality which is based on the number of nodes and their links inside a community versus the community size further reported to the size of the network. A novel aspect of the proposed fitness function refers to considering the way nodes connect to other nodes inside the same community making this second level of links contribute to the strength of the community. The introduced fitness function is tested inside a collaborative evolutionary algorithm specifically designed for the problem of community detection in complex networks. Computational experiments are performed for several real-world complex networks which have a known real community structure. This allows the direct verification of the quality of evolved communities via the proposed fitness function emphasizing extremely promising numerical results.