The task of community detection, which aims to partition a network into clusters of nodes to summarize its large-scale structure, has spawned the development of many competing algorithms with varying objectives. Some community detection methods are inferential, explicitly deriving the clustering objective through a probabilistic generative model, while other methods are descriptive, dividing a network according to an objective motivated by a particular application, making it challenging to compare these methods on the same scale. Here we present a solution to this problem that associates any community detection objective, inferential or descriptive, with its corresponding implicit network generative model. This allows us to compute the description length of a network and its partition under arbitrary objectives, providing a principled measure to compare the performance of different algorithms without the need for "ground truth" labels. Our approach also gives access to instances of the community detection problem that are optimal to any given algorithm, and in this way reveals intrinsic biases in popular descriptive methods, explaining their tendency to overfit. Using our framework, we compare a number of community detection methods on artificial networks, and on a corpus of over 500 structurally diverse empirical networks. We find that more expressive community detection methods exhibit consistently superior compression performance on structured data instances, without having degraded performance on a minority of situations where more specialized algorithms perform optimally. Our results undermine the implications of the "no free lunch" theorem for community detection, both conceptually and in practice, since it is confined to unstructured data instances, unlike relevant community detection problems which are structured by requirement.

翻译：社区检测任务旨在将网络划分为节点簇，以总结其大规模结构，由此催生了众多目标各异的竞争算法。部分社区检测方法具有推断性，通过概率生成模型显式推导聚类目标；而其他方法则具有描述性，基于特定应用动机的目标对网络进行划分——这使得在不同尺度上比较这些方法存在挑战。本文提出一种解决方案：将任意社区检测目标（无论推断性或描述性）与其对应的隐式网络生成模型相关联。据此，我们可在任意目标下计算网络及其划分的描述长度，为无需“真实标签”即可比较不同算法性能提供原则性度量。该方法还能为给定算法生成最优的社区检测问题实例，进而揭示主流描述性方法的内在偏差，解释其过拟合倾向。利用该框架，我们在人工网络和涵盖500余个结构多样实证网络的语料库上比较了多种社区检测方法。研究发现：更具表达力的社区检测方法在结构化数据实例上始终表现出更优的压缩性能，且不会在少数专业化算法表现最佳的情景中性能退化。我们的结果在概念与实践层面均动摇了社区检测中“没有免费午餐”定理的推论——该定理仅局限于非结构化数据实例，而相关社区检测问题必然具有结构特征。