Large-scale curvature of networks.

Understanding key structural properties of large-scale networks is crucial for analyzing and optimizing their performance and improving their reliability and security. Here, through an analysis of a collection of data networks across the globe as measured and documented by previous researchers, we show that communications networks at the Internet protocol (IP) layer possess global negative curvature. We show that negative curvature is independent of previously studied network properties, and that it has a major impact on core congestion: the load at the core of a finite negatively curved network with N nodes scales as N(2), as compared to N(1.5) for a generic finite flat network.