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Community detection methods attempt to divide a network into groups of nodesthat share similar properties, thus revealing its large-scale structure. Amajor challenge when employing such methods is that they are often degenerate,typically yielding a complex landscape of competing answers. As an attempt toextract understanding from a population of alternative solutions, many methodsexist to establish a consensus among them in the form of a single partition"point estimate" that summarizes the whole distribution. Here we show that itis in general not possible to obtain a consistent answer from such pointestimates when the underlying distribution is too heterogeneous. As analternative, we provide a comprehensive set of methods designed to characterizeand summarize complex populations of partitions in a manner that captures notonly the existing consensus, but also the dissensus between elements of thepopulation. Our approach is able to model mixed populations of partitions wheremultiple consensuses can coexist, representing different competing hypothesesfor the network structure. We also show how our methods can be used to comparepairs of partitions, how they can be generalized to hierarchical divisions, andbe used to perform statistical model selection between competing hypotheses.

Revealing consensus and dissensus between network partitions