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 how they can be used to perform statistical model selection between competing hypotheses.

中文翻译：

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揭示网络分区之间的共识和分歧

社区检测方法试图将网络划分为共享相似属性的节点组，从而揭示其大规模结构。使用此类方法时的主要挑战是它们通常会退化，通常会产生竞争性答案的复杂局面。为了从众多替代解决方案中提取理解，存在许多方法可以在单个解决方案中建立共识，以单个分区“点估计”的形式总结整个分布。在这里，我们表明，当基础分布过于异构时，通常无法从此类点估计中获得一致的答案。作为备选，我们提供了一套全面的方法，旨在以既捕获现有共识又捕获总体元素之间的分歧的方式来表征和汇总复杂的分区总体。我们的方法能够对分区的混合总体进行建模，其中多个共识可以共存，代表网络结构的不同竞争假设。我们还将展示如何将我们的方法用于比较分区对，如何将其推广到层次划分以及如何将其用于在竞争假设之间进行统计模型选择。代表网络结构的不同竞争假设。我们还将展示如何将我们的方法用于比较分区对，如何将其推广到层次划分以及如何将其用于在竞争假设之间进行统计模型选择。代表网络结构的不同竞争假设。我们还将展示如何将我们的方法用于比较分区对，如何将其推广到层次划分以及如何将其用于在竞争假设之间进行统计模型选择。