Pattern Detection in Complex Networks: Correlation Profile of the Internet

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Abstract
A general scheme for detecting and analyzing topological patterns in complex networks is presented. To this end one first generates a randomized version of a given network which preserves some of its low-level topological properties, such as e.g. connectivities of individual nodes, and does not allow for multiple edges between the same pair of nodes. One then concentrates only on those higher level properties of the complex network in question that significantly deviate from the above null model, and, therefore, likely reflect its basic design principles and/or evolutionary history. Our general methods allow us to measure the correlation profile of the Internet quantifying correlations between connectivities of neighboring nodes. This profile was found to be qualitatively different from that previously reported for molecular networks. It was further demonstrated that the level of clustering of the Internet is very sensitive to both the connectivity distribution and its correlation profile and is some 60 percent higher than in a random network preserving both these properties.

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