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聚类以总结其大规模结构，这一任务催生了多种目标各异的竞争性算法。部分社区检测方法属于推断型方法，通过概率生成模型显式推导聚类目标；而其他方法属于描述型方法，则根据特定应用场景驱动的目标划分网络。这使得在统一尺度下比较这些方法面临挑战。本文提出一种解决方案，能够将任何社区检测目标（无论是推断型还是描述型）与其对应的隐式网络生成模型相关联。通过这一方案，我们可以在任意目标下计算网络及其划分的描述长度，从而提供一种无需依赖"真实标签"即可比较不同算法性能的规范化度量。我们的方法还能获取对任意给定算法最优的社区检测问题实例，并由此揭示流行描述型方法的内在偏向，解释其过度拟合的倾向。利用这一框架，我们在人工网络以及超过500个结构多样的实证网络语料库上比较了多种社区检测方法。研究发现，表达能力更强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，而在少数专业算法表现最优的情形中，其性能并未下降。我们的结果不仅在概念层面也在实践层面削弱了社区检测中"无免费午餐"定理的推论——该定理局限于非结构化数据实例，而相关社区检测问题恰恰通过需求呈现出结构化特征。