Generative models for two-ground-truth partitions in networks

A myriad of approaches have been proposed to characterise the mesoscale structure of networks - most often as a partition based on patterns variously called communities, blocks, or clusters. Clearly, distinct methods designed to detect different types of patterns may provide a variety of answers to the network's mesoscale structure. Yet, even multiple runs of a given method can sometimes yield diverse and conflicting results, yielding entire landscapes of partitions which potentially include multiple (locally optimal) mesoscale explanations of the network. Such ambiguity motivates a closer look at the ability of these methods to find multiple qualitatively different 'ground truth' partitions in a network. Here, we propose a generative model which allows for two distinct partitions to be built into the mesoscale structure of a single benchmark network. We demonstrate a use case of the benchmark model by exploring the power of stochastic block models (SBMs) to detect coexisting bi-community and core-periphery structures of different strengths. We find that the ability to detect the two partitions individually varies considerably by SBM variant and that coexistence of both partitions is recovered only in a very limited number of cases. Our findings suggest that in most instances only one - in some way dominating - structure can be detected, even in the presence of other partitions in the generated network. They underline the need for considering entire landscapes of partitions when different competing explanations exist and motivate future research to advance partition coexistence detection methods. Our model also contributes to the field of benchmark networks more generally by enabling further exploration of the ability of new and existing methods to detect ambiguity in mesoscale structure of networks.