Pattern Detection in Complex Networks: Correlation Profile of the Internet

TL;DR

This paper introduces a method for detecting topological patterns in large complex networks by comparing them with randomized models, and applies it to analyze the Internet's correlation profile, revealing unique structural features.

Contribution

It presents a novel scheme for analyzing network patterns through null models and applies it to the Internet, highlighting its distinct correlation profile.

Findings

The Internet's correlation profile differs from molecular networks with similar degree distributions.

Clustering in the Internet is highly sensitive to its connectivity and correlation profile.

The method effectively distinguishes the Internet's topology from randomized models.

Abstract

A general scheme for detecting and analyzing topological patterns in large complex networks is presented. In this scheme the network in question is compared with its properly randomized version that preserves some of its low-level topological properties. Statistically significant deviation of any measurable property of a network from this null model likely reflect its design principles and/or evolutionary history. We illustrate this basic scheme on the example of the correlation profile of the Internet quantifying correlations between connectivities of its neighboring nodes. This profile distinguishes the Internet from previously studied molecular networks with a similar scale-free connectivity distribution. We finally demonstrate that clustering in a network is very sensitive to both the connectivity distribution and its correlation profile and compare the clustering in the Internet to the appropriate null model.