Source-linked AI summary
The Large Scale Curvature of Networks
Onuttom Narayan, Iraj Saniee
TL;DR
Large-scale networks require structural properties that clarify performance, reliability, and security, but global curvature had not been directly measured at the IP layer. The paper measures curvature in real networks and analyzes geodesic load, finding core load scales as N^2 rather than N^1.5 for flat networks.
Problem
Large-scale networks need structural properties that support reliable analysis of performance, reliability, and security.
Method
The paper defines finite-network global negative curvature, measures it directly in numerous publicly available IP-layer network topologies, and analyzes geodesic traffic load.
Results
N^2 core-load scaling in hyperbolic networks exceeds the N^1.5 scaling found for flat networks.
Takeaways & Limitations
Hyperbolicity is distinct from degree distribution, entails small-world behavior, and can significantly affect network performance through core congestion.
Takeaways & Limitations
The studied networks have edge-to-node ratios from 1.27 to 2.72, so the observed central concentration is not attributable to networks being almost simple trees.
Abstract
from arXiv · showhide
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.