Exploring partition diversity in complex networks

Partition diversity refers to the concept that for some networks there may be multiple, similarly plausible ways to group the nodes, rather than one single best partition. In this talk, I will present two projects that address this idea from different but complementary angles. The first introduces the benchmark stochastic cross-block model (SCBM), a generative model designed to create synthetic networks with two distinct 'ground-truth' partitions. This allows us to study the extent to which existing methods for partition detection are able to reveal the coexistence of multiple underlying structures. The second project builds on this benchmark and paves the way for a Bayesian inference framework to directly detect coexisting partitions in empirical networks. By formulating this model as a microcanonical variant of the SCBM, we can evaluate how well it fits a given network compared to existing models. We find that our method more reliably detects partition diversity in synthetic networks with planted coexisting partitions, compared to methods designed to detect a single optimal partition. Together, the two projects contribute to a broader understanding of partition diversity by offering tools to explore the ambiguity of network structure.