Revealing consensus and dissensus between network partitions

TL;DR

This paper introduces methods to analyze and summarize diverse sets of network partitions, capturing both consensus and disagreement, especially in heterogeneous populations, to better understand complex network structures.

Contribution

It presents novel techniques for characterizing and comparing multiple network partitions, including modeling mixed populations and hierarchical divisions, beyond traditional consensus methods.

Findings

Methods effectively capture consensus and dissensus in partition populations

Approach models multiple coexisting hypotheses in network structures

Techniques enable statistical comparison and model selection of partitions

Abstract

Community detection methods attempt to divide a network into groups of nodes that share similar properties, thus revealing its large-scale structure. A major challenge when employing such methods is that they are often degenerate, typically yielding a complex landscape of competing answers. As an attempt to extract understanding from a population of alternative solutions, many methods exist to establish a consensus among them in the form of a single partition "point estimate" that summarizes the whole distribution. Here we show that it is in general not possible to obtain a consistent answer from such point estimates when the underlying distribution is too heterogeneous. As an alternative, we provide a comprehensive set of methods designed to characterize and summarize complex populations of partitions in a manner that captures not only the existing consensus, but also the dissensus between elements of the population. Our approach is able to model mixed populations of partitions where multiple consensuses can coexist, representing different competing hypotheses for the network structure. We also show how our methods can be used to compare pairs of partitions, how they can be generalized to hierarchical divisions, and be used to perform statistical model selection between competing hypotheses.