The Large Scale Curvature of Networks

Abstract

Understanding key structural properties of large scale networks are crucial for analyzing and optimizing their performance, and improving their reliability and security. Here we show that these networks possess a previously unnoticed feature, global curvature, which we argue has a major impact on core congestion: the load at the core of a network with N nodes scales as N^2 as compared to N^1.5 for a flat network. We substantiate this claim through analysis of a collection of real data networks across the globe as measured and documented by previous researchers.

4 pages, 5 figures

References in corpus (6)

• Hyperbolic Geometry of Complex Networks
• Optimal routing on complex networks
• Curvature and temperature of complex networks
• Transport optimization on complex networks
• Impact of community structure on information transfer
• Congestion diffusion and decongestion strategy in networked traffic

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