标题： 基于最大熵划分和重正化群的分层社区检测 显示英文标题

标题： Hierarchical community detection via maximum entropy partitions and the renormalization group

摘要： 在多个尺度上识别有意义的结构仍然是网络科学中的一个核心挑战。 我们引入了分层聚类熵（Hierarchical Clustering Entropy，HCE），这是一个通用且与模型无关的框架，用于检测分层社区结构中的信息层次。 与现有方法不同，HCE直接作用于树状图，而无需依赖边级统计量。 它选择能够最大化社区大小分布的熵与社区数量之间合理权衡的分辨率层次，对应于高结构异质性的尺度。 这一标准适用于由多种聚类算法和距离度量生成的树状图，包括基于模块度和基于相关性的方法。 我们在具有不同层次程度、规模不平衡和噪声的合成基准上评估HCE，包括LFR以及对称和非对称多尺度模型，并表明它始终能识别出与真实情况高度一致的划分。 应用于社会和神经科学系统中的现实网络时，HCE揭示了与已知结构和功能组织相一致的可解释模块层次。 作为一种可扩展且有原则的方法，HCE提供了一种通用的、领域无关的分层社区检测方法，具有在生物、社会和技术系统中潜在的应用前景。 显示英文摘要

摘要： Identifying meaningful structure across multiple scales remains a central challenge in network science. We introduce Hierarchical Clustering Entropy (HCE), a general and model-agnostic framework for detecting informative levels in hierarchical community structures. Unlike existing approaches, HCE operates directly on dendrograms without relying on edge-level statistics. It selects resolution levels that maximize a principled trade-off between the entropy of the community size distribution and the number of communities, corresponding to scales of high structural heterogeneity. This criterion applies to dendrograms produced by a wide range of clustering algorithms and distance metrics, including modularity-based and correlation-based methods. We evaluate HCE on synthetic benchmarks with varying degrees of hierarchy, size imbalance, and noise, including LFR and both symmetric and asymmetric multiscale models, and show that it consistently identifies partitions closely aligned with ground truth. Applied to real-world networks in social and neuroscience systems, HCE reveals interpretable modular hierarchies that align with known structural and functional organizations. As a scalable and principled method, HCE offers a general, domain-independent approach to hierarchical community detection with potential applications across biological, social, and technological systems.