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.