  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.
