Class of correlated random 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.
Keywords
Cite
@article{arxiv.cond-mat/0306072,
title = {Class of correlated random networks with hidden variables},
author = {Marian Boguna and Romualdo Pastor-Satorras},
journal= {arXiv preprint arXiv:cond-mat/0306072},
year = {2009}
}