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 is they are often degenerate, typically yielding complex landscape competing answers. As an extract understanding from population alternative solutions, many exist establish consensus among them in the form single partition "point estimate" summarizes whole distribution. Here we show it general not possible obtain consistent answer point estimates underlying distribution too heterogeneous. alternative, provide comprehensive set designed characterize and summarize populations partitions manner captures only existing consensus, but also dissensus between elements population. Our approach able model mixed where multiple consensuses can coexist, representing different hypotheses for We how our be used compare pairs partitions, generalized hierarchical divisions, perform statistical selection hypotheses.