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.

翻译：为表征网络的中尺度结构，学界提出了大量方法——最常见的是基于模式（如社区、块或聚类）的划分方法。显然，旨在检测不同类型模式的不同方法可能对网络的中尺度结构给出多种答案。然而，即便对同一方法进行多次运行，有时也会产生不同甚至冲突的结果，形成可能包含多个（局部最优）中尺度解释的划分全景。这种模糊性促使我们更深入地审视这些方法在网络中发现多个性质不同的"真实"划分的能力。本文提出一种生成模型，该模型允许在单一基准网络的中尺度结构中内置两种不同的划分。我们通过探索随机块模型（SBM）检测不同强度下共存的双社区结构与核心-边缘结构的能力，展示了该基准模型的应用案例。研究发现，检测这两种划分的能力因SBM变体而异，且仅在极少数情况下能恢复两种划分的共存状态。我们的结果表明，在大多数情况下，即使生成网络中存在其他划分，也仅能检测到某种具有主导地位的结构。这凸显了当存在不同竞争性解释时需考虑整个划分全景的必要性，并为推进划分共存检测方法的研究提供了动机。从更广泛的基准网络领域来看，我们的模型通过支持进一步探索新旧方法检测网络中尺度结构模糊性的能力，也做出了相应贡献。