Researchers theorize that many real-world networks exhibit community structure where within-community edges are more likely than between-community edges. While numerous methods exist to cluster nodes into different communities, less work has addressed this question: given some network, does it exhibit statistically meaningful community structure? We answer this question in a principled manner by framing it as a statistical hypothesis test in terms of a general and model-agnostic community structure parameter. Leveraging this parameter, we propose a simple and interpretable test statistic used to formulate two separate hypothesis testing frameworks. The first is an asymptotic test against a baseline value of the parameter while the second tests against a baseline model using bootstrap-based thresholds. We prove theoretical properties of these tests and demonstrate how the proposed method yields rich insights into real-world datasets.

中文翻译：

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网络中社区结构的广义假设检验

研究人员推测，许多现实世界的网络都表现出社区结构，其中社区内边缘比社区间边缘更有可能出现。虽然存在多种将节点聚类到不同社区的方法，但解决这个问题的工作却很少：给定一些网络，它是否表现出有统计学意义社区结构？我们以原则性的方式回答这个问题，将其框架为根据一般且与模型无关的社区结构参数进行统计假设检验。利用这个参数，我们提出了一个简单且可解释的检验统计量，用于制定两个独立的假设检验框架。第一个是针对参数基线值的渐近测试，而第二个是使用基于引导程序的阈值针对基线模型进行测试。我们证明了这些测试的理论特性，并演示了所提出的方法如何对现实世界的数据集产生丰富的见解。