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Community structure is one of the most important features of complexnetworks. Modularity-based methods for community detection typically rely onheuristic algorithms to optimize a specific community quality function. Suchmethods are limited by two major defects: (1) the resolution limit problem,which prohibits communities of heterogeneous sizes being simultaneouslydetected, and (2) divergent outputs of the heuristic algorithm, which make itdifficult to differentiate relevant and irrelevant results. In this paper, wepropose an improved method for community detection based on a scalablecommunity "fitness function." We introduced a new parameter to enhance itsscalability, and a strict strategy to filter the outputs. Due to thescalability, on the one hand our method is free of the resolution limit problemand performs excellently on large heterogeneous networks, while on the otherhand it is capable of detecting more levels of communities than previousmethods in deep hierarchical networks. Moreover, our strict strategyautomatically removes redundant and irrelevant results, without any artificialselection. As a result, our method neatly outputs only the stable and uniquecommunities, which are largely interpretable by the a priori knowledge aboutthe network, including the implanted structures within synthetic networks, ormetadata for real-world networks.

Automatic detection of multilevel communities: scalable and resolution-limit-free