Class of correlated random networks with hidden variables

TL;DR

This paper introduces a class of correlated random network models using hidden variables, providing analytical expressions for their properties, and extends the models to generate networks with specified correlations and growth dynamics.

Contribution

It develops a general analytical framework for correlated random networks with hidden variables and proposes algorithms for network generation with desired correlation structures.

Findings

Analytical expressions for network properties as functions of hidden variable distribution.

Numerical validation of the models through simulations.

Extension to model non-equilibrium growing networks with hidden variables.

Abstract

We study a class models of correlated random networks in which vertices are characterized by \textit{hidden variables} controlling the establishment of edges between pairs of vertices. We find analytical expressions for the main topological properties of these models as a function of the distribution of hidden variables and the probability of connecting vertices. The expressions obtained are checked by means of numerical simulations in a particular example. The general model is extended to describe a practical algorithm to generate random networks with an \textit{a priori} specified correlation structure. We also present an extension of the class, to map non-equilibrium growing networks to networks with hidden variables that represent the time at which each vertex was introduced in the system.