title: Community detection in networks with unequal groups.
abstract: Recently, a phase transition has been discovered in the network community detection problem below which no algorithm can tell which nodes belong to which communities with success any better than a random guess. This result has, however, so far been limited to the case where the communities have the same size or the same average degree. Here we consider the case where the sizes or average degrees differ. This asymmetry allows us to assign nodes to communities with better-than-random success by examining their local neighborhoods. Using the cavity method, we show that this removes the detectability transition completely for networks with four groups or fewer, while for more than four groups the transition persists up to a critical amount of asymmetry but not beyond. The critical point in the latter case coincides with the point at which local information percolates, causing a global transition from a less-accurate solution to a more-accurate one.
authors: Santa Fe Institute, Santa Fe, New Mexico 87501, USA.|State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China.
authors: Pan
authors: P
authors: Zhang
authors: Santa Fe Institute, Santa Fe, New Mexico 87501, USA.
authors: Cristopher
authors: C
authors: Moore
authors: Santa Fe Institute, Santa Fe, New Mexico 87501, USA.|Physics Department and the Center for the Study of Complex Systems, University of Michigan, Ann Arbor, Michigan 48109, USA.
authors: M E J
authors: ME
authors: Newman