Networks with given two-point correlations: hidden correlations from degree correlations

Abstract

The paper orders certain important issues related to both uncorrelated and correlated networks with hidden variables. In particular, we show that networks being uncorrelated at the hidden level are also lacking in correlations between node degrees. The observation supported by the depoissonization idea allows to extract distribution of hidden variables from a given node degree distribution. It completes the algorithm for generating uncorrelated networks that was suggested by other authors. In this paper we also carefully analyze the interplay between hidden attributes and node degrees. We show how to extract hidden correlations from degree correlations. Our derivations provide mathematical background for the algorithm for generating correlated networks that was proposed by Boguna and Pastor-Satorras.

APS twocolumn style, 10 pages, 5 figures

References in corpus (14)

• Emergence of scaling in random networks
• Statistical mechanics of complex networks
• Assortative mixing in networks
• Random graphs with arbitrary degree distributions and their applications
• Mixing patterns in networks
• Mean-field theory for scale-free random networks
• Universal Behavior of Load Distribution in Scale-free Networks
• Class of correlated random networks with hidden variables
• A General Formalism for Inhomogeneous Random Graphs
• The origin of degree correlations in the Internet and other networks
• Statistical ensemble of scale-free random graphs
• Random Graphs with Hidden Color
• Properties of Random Graphs with Hidden Color
• How to calculate the main characteristics of random uncorrelated networks

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