The hyperbolic network models exhibit very fundamental and essential features, like small-worldness, scale-freeness, high-clustering coefficient, and community structure. In this paper, we comprehensively explore the presence of an important feature, the core-periphery structure, in the hyperbolic network models, which is often exhibited by real-world networks. We focused on well-known hyperbolic models such as popularity-similarity optimization model (PSO) and S1/H2 models and studied core-periphery structures using a well-established method that is based on standard random walk Markov chain model. The observed core-periphery centralization values indicate that the core-periphery structure can be very pronounced under certain conditions. We also validate our findings by statistically testing for the significance of the observed core-periphery structure in the network geometry. This study extends network science and reveals core-periphery insights applicable to various domains, enhancing network performance and resiliency in transportation and information systems.

翻译：双曲网络模型展现出诸多基础且本质的特征，如小世界性、无标度性、高聚类系数及社区结构。本文系统探究了双曲网络模型中一个重要特征——核心-边缘结构的存在性，该结构在现实世界网络中普遍存在。我们聚焦于经典双曲模型（如流行度-相似度优化模型（PSO）与S1/H2模型），并采用基于标准随机游走马尔可夫链模型的成熟方法研究其核心-边缘结构。观测到的核心-边缘中心化数值表明，在特定条件下该结构可能极为显著。我们进一步通过统计检验验证了网络几何中观测到的核心-边缘结构的显著性。本研究拓展了网络科学领域，所揭示的核心-边缘结构洞见可应用于多学科领域，有助于提升交通与信息系统的网络性能与鲁棒性。