Defining least community as a homogeneous group in complex networks

•A new community detection algorithm inspired by the head/tail breaks.•A new way of thinking for community detection or classification in general.•Far more small communities than large ones in complex networks.•Simple networks like mechanical watches, while complex networks like human brains.•Empirical evidence on power laws of the detected communities.

This paper introduces a new concept of least community that is as homogeneous as a random graph, and develops a new community detection algorithm from the perspective of homogeneity or heterogeneity. Based on this concept, we adopt head/tail breaks–a newly developed classification scheme for data with a heavy-tailed distribution–and rely on edge betweenness given its heavy-tailed distribution to iteratively partition a network into many heterogeneous and homogeneous communities. Surprisingly, the derived communities for any self-organized and/or self-evolved large networks demonstrate very striking power laws, implying that there are far more small communities than large ones. This notion of far more small things than large ones constitutes a new fundamental way of thinking for community detection.