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Detecting communities in networks and graphs is an important task across manydisciplines such as statistics, social science and engineering. There aregenerally three different kinds of mixing patterns for the case of twocommunities: assortative mixing, disassortative mixing and core-peripherystructure. Modularity optimization is a classical way for fitting networkmodels with communities. However, it can only deal with assortative mixing anddisassortative mixing when the mixing pattern is known and fails to discoverthe core-periphery structure. In this paper, we extend modularity in astrategic way and propose a new framework based on Unified Bigroups StandadizedEdge-count Analysis (UBSea). It can address all the formerly mentionedcommunity mixing structures. In addition, this new framework is able toautomatically choose the mixing type to fit the networks. Simulation studiesshow that the new framework has superb performance in a wide range of settingsunder the stochastic block model and the degree-corrected stochastic blockmodel. We show that the new approach produces consistent estimate of thecommunities under a suitable signal-to-noise-ratio condition, for the case of ablock model with two communities, for both undirected and directed networks.The new method is illustrated through applications to several real-worlddatasets.

UBSea: A Unified Community Detection Framework