Hyperbolic network models exhibit very fundamental and essential features, like small worldness, scale freeness, a 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 the popularity-similarity optimization model (PSO) and ${\mathbb{S}}^1\text{/}{\mathbb{H}}^2$ models and studied core-periphery structures using well-established methods. 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.

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• Network stability
• Network structure
• Phase transitions