标题： 具有任意介观结构的随机双曲图 显示英文标题

标题： Random Hyperbolic Graphs with Arbitrary Mesoscale Structures

摘要： 现实世界中的网络表现出一些通用的结构特性，比如稀疏性、小世界效应、异质度分布、高聚类性和社区结构。 几何网络模型，特别是随机双曲图（RHGs），通过将节点嵌入潜在的相似性空间中，能够有效捕捉到许多这些特性。 然而，网络通常由节点组之间的特定连接模式——即社区——所定义，这些社区并非几何意义上的，因为组与组之间的差异并不服从三角不等式。 因此，仅仅基于相似性和流行度之间的相互作用来构建连接，对RHGs能生成的网络的中观结构存在根本性的限制。 为了解决这一限制，我们引入了随机双曲块模型（RHBM），它通过在最大熵框架内引入块状结构扩展了RHGs。 我们通过合成网络分析展示了RHBM的优势，强调了它在保留社区结构方面的能力，而纯几何模型在此处失败。 我们的研究结果强调了潜在几何学在网络建模中的重要性，同时解决了其在控制中观混合模式方面的局限性。 显示英文摘要

摘要： Real-world networks exhibit universal structural properties such as sparsity, small-worldness, heterogeneous degree distributions, high clustering, and community structures. Geometric network models, particularly Random Hyperbolic Graphs (RHGs), effectively capture many of these features by embedding nodes in a latent similarity space. However, networks are often characterized by specific connectivity patterns between groups of nodes -- i.e. communities -- that are not geometric, in the sense that the dissimilarity between groups do not obey the triangle inequality. Structuring connections only based on the interplay of similarity and popularity thus poses fundamental limitations on the mesoscale structure of the networks that RHGs can generate. To address this limitation, we introduce the Random Hyperbolic Block Model (RHBM), which extends RHGs by incorporating block structures within a maximum-entropy framework. We demonstrate the advantages of the RHBM through synthetic network analyses, highlighting its ability to preserve community structures where purely geometric models fail. Our findings emphasize the importance of latent geometry in network modeling while addressing its limitations in controlling mesoscale mixing patterns.