Revealing Consensus and Dissensus between Network Partitions

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 how they can be used to perform statistical model selection between competing hypotheses.

Automated summary

Community detection methods aim to divide a network into groups with similar properties, but often face challenges in yielding consistent answers. Instead of relying on single partition point estimates, this study presents a comprehensive set of methods to characterize and summarize complex populations of partitions, capturing both consensus and dissensus within the population. The approach can model mixed populations of partitions, compare pairs of partitions, generalize to hierarchical divisions, and perform statistical model selection between competing hypotheses for network structure.