Weighted modularity optimization for crisp and fuzzy community detection in large-scale networks

Community detection is a classic and very difficult task in the field of complex network analysis, principally for its applications in domains such as social or biological networks analysis. One of the most widely used technologies for community detection in networks is the maximization of the quality function known as modularity. However, existing work has proved that modularity maximization algorithms for community detection may fail to resolve communities in small size. Here we present a new community detection method, which is able to find crisp and fuzzy communities in undirected and unweighted networks by maximizing weighted modularity. The algorithm derives new edge weights using the cosine similarity in order to go around the resolution limit problem. Then a new local moving heuristic based on weighted modularity optimization is proposed to cluster the updated network. Finally, the set of potentially attractive clusters for each node is computed, to further uncover the crisply fuzzy partition of the network. We give demonstrative applications of the algorithm to a set of synthetic benchmark networks and six real-world networks and find that it outperforms the current state of the art proposals (even those aimed at finding overlapping communities) in terms of quality and scalability.

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