Characterizing the Analogy Between Hyperbolic Embedding and Community Structure of Complex Networks

Area of Science:

• Network science
• Complex systems
• Data analysis

Background:

• Hyperbolic geometry is increasingly used for network embedding.
• Community structure is a fundamental property of many real-world networks.
• Understanding the relationship between these concepts is crucial for network analysis.

Purpose of the Study:

• To demonstrate that network community structure can serve as a coarse approximation of hyperbolic geometry embeddings.
• To reinterpret existing network hyperbolic embedding results using only community structure.
• To explore applications of this analogy in network robustness and navigability.

Main Methods:

• Systematic analysis of real-world and synthetic networks.
• Leveraging the analogy between community structure and hyperbolic embeddings.
• Investigating multiplex network robustness by correlating community structures across layers.
• Developing a greedy protocol for network navigability using community-based routing tables.

Main Results:

• Network community structure effectively approximates hyperbolic embeddings.
• Multiplex network robustness can be controlled by inter-layer community structure correlation.
• A greedy routing protocol based on community structure improves network navigability.

Conclusions:

• Community structure provides a valuable, simplified lens for understanding hyperbolic network properties.
• The findings offer practical implications for designing robust and navigable complex networks.
• This work bridges the gap between community detection and hyperbolic network embedding.