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Hyperbolicity measures democracy in real-world networks.
Michele Borassi1, Alessandro Chessa2, Guido Caldarelli3
1IMT Institute for Advanced Studies, Piazza San Francesco 19, 55100 Lucca, Italy.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 15, 2015
Summary
This study explores network hyperbolicity, revealing aristocratic (few hubs) vs. democratic (many hubs) structures. It introduces "influence area" to differentiate local and global networks based on connectivity.
Area of Science:
- Network Science
- Graph Theory
- Geometric Measure Theory
Background:
- Hyperbolicity quantifies negative curvature in spaces.
- Understanding network structure is crucial for analyzing complex systems.
Purpose of the Study:
- To analyze the hyperbolicity of real-world networks.
- To provide new interpretations and measures for network structure.
- To define and analyze the
- influence area
- of network nodes.
Main Methods:
- Analysis of network hyperbolicity.
- Introduction of average hyperbolicity of neighbors.
- Classification of networks into 'local' and 'global' types.
Main Results:
- Hyperbolic networks exhibit an 'aristocratic' structure (few key nodes).
- Non-hyperbolic networks show a 'democratic' structure (more distributed key nodes).
- The 'influence area' of high-degree nodes is small in local networks (e.g., social networks) and large in global networks (e.g., power grids).
Conclusions:
- Network hyperbolicity offers a novel lens for network analysis.
- The 'influence area' concept effectively distinguishes network types.
- Findings have implications for understanding information flow and system resilience in diverse networks.
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