Local multiresolution order in community detection

Multi-scale (“multiresolution”) community detection attempts to identify the most relevant divisions (groups of related nodes) of an arbitrary network over a range of network scales. This task is generally accomplished by analyzing community stability in an average sense across all communities in the network. In some systems, contending partitions of the global community structure may be vague or imprecisely defined, but certain local communities may nevertheless be strongly correlated at a given network resolution. We demonstrate a general local multiresolution method where we draw inferences about local community “strength” based on correlations between clusters in independently-solved systems. We propose measures analogous to variation of information and normalized mutual information which quantitatively identify the best resolution(s) at the community level. Our approach is independent of the applied community detection algorithm save for the inherent requirement that the method be able to identify communities across different network scales. It should, in principle, easily adapt to alternate community comparison measures.