Detection of topological patterns in complex networks: correlation profile of the internet

By S. Maslov, K. Sneppen, A. Zaliznyak. 2002

313 citations recorded by the source corpus.

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 topological property of a network from this null model likely reflects its design principles and/or evolutionary history. We illustrate this basic scheme using the example of the correlation profile of the Internet quantifying correlations between degrees of its neighboring nodes. This profile distinguishes the Internet from previously studied molecular networks with a similar scale-free degree distribution. We finally demonstrate that the clustering in a network is very sensitive to both the degree distribution and its correlation profile and compare the clustering in the Internet to the appropriate null model.

Subfields: Molecular Biology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/1ecb903439b62172ed10838d82ddb4ff9e0ec43f

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In Molecular Biology

In Statistical and Nonlinear Physics

Citations in the corpus

The statistical physics of real-world networks (2018, background): “[45] S.”
The Anatomy of the Facebook Social Graph (2011, background): “However, we can do more than measure these simple statistics and we characterize the conditional probability p(k|k) that a randomly chosen friend of an individual with degree k has degree k [35].”
Classes of complex networks defined by role-to-role connectivity profiles. (2007, background): “As some simple properties such as the degree and the clustering coefficient trivially depend on a node’s role, we focus on degree–degree correlation”
Popularity versus similarity in growing networks (2011, methodology): “For each network we then perform a number of random link rewirings preserving the degree distribution in the network and trying to increase its clustering if possible [52].”
Contact Patterns among High School Students (2014, background): “We also consider edge rewirings which conserve the degree of each node (‘‘Sneppen-Maslov’’ null model [36]), once again either (a) globally or (b) separately for each class pair.”
Cut-offs and finite size effects in scale-free networks (2003, methodology): “For SF networks with exponent t [29] as it can be shown by applying the reasoning concerning the scaling of the degree distribution cut-off.”
Analyzing and modeling real-world phenomena with complex networks: a survey of applications (2007, background): “[189] to identify differences in networks with the same degree distribution, such as the Internet at AS level (in 2000) and molecular networks.”
What's in a crowd? Analysis of face-to-face behavioral networks (2010, methodology): “To this end, we construct a randomized network using the rewiring procedure described by Maslov et al. (2004).”