Uncovering the hidden core-periphery structure in hyperbolic networks

Area of Science:

• Network Science
• Complex Systems
• Graph Theory

Background:

• Hyperbolic network models possess key real-world network features like scale-freeness and community structure.
• The core-periphery structure is a significant organizational principle observed in many real-world networks.
• Understanding this structure in hyperbolic models is crucial for network analysis and design.

Purpose of the Study:

• To investigate the presence and characteristics of core-periphery structure in hyperbolic network models.
• To analyze how well-known hyperbolic models, such as the popularity-similarity optimization (PSO) and S¹/H² models, exhibit core-periphery organization.
• To statistically validate the significance of the observed core-periphery structure within the network geometry.

Main Methods:

• Utilized established methods for analyzing network structure.
• Focused on the popularity-similarity optimization (PSO) and S¹/H² hyperbolic network models.
• Calculated core-periphery centralization values and performed statistical significance testing.

Main Results:

• The study observed pronounced core-periphery structures in hyperbolic network models under specific conditions.
• Core-periphery centralization values were analyzed to quantify the structure's prominence.
• Statistical tests confirmed the significance of the core-periphery structure within the network geometry.

Conclusions:

• Hyperbolic network models can exhibit significant core-periphery structures, mirroring real-world network properties.
• The findings contribute to network science by elucidating core-periphery organization in hyperbolic settings.
• Insights gained can enhance the design and resilience of transportation and information systems.