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

TL;DR

This paper explores the relationship between hidden variables and degree correlations in networks, providing methods to extract hidden correlations from degree data and enhancing algorithms for generating correlated networks.

Contribution

It introduces a mathematical framework to analyze and extract hidden correlations from degree correlations, extending existing algorithms for network generation.

Findings

Networks uncorrelated at the hidden level lack degree correlations

Method to extract hidden variable distribution from degree distribution

Mathematical basis for generating correlated networks

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.