Measuring Significance of Community Structure in Complex Networks

Many complex systems can be represented as networks and separating a network into communities could simplify the functional analysis considerably. Recently, many approaches have been proposed for finding communities, but none of them can evaluate the communities found are significant or trivial definitely. In this paper, we propose an index to evaluate the significance of communities in networks. The index is based on comparing the similarity between the original community structure in network and the community structure of the network after perturbed, and is defined by integrating all the similarities. Many artificial networks and real-world networks are tested. The results show that the index is independent from the size of network and the number of communities. Moreover, we find the clear communities always exist in social networks, but don't find significative communities in proteins interaction networks and metabolic networks.