Towards correlated random networks

TL;DR

This paper introduces models of correlated random networks with adjustable correlation ranges, analyzes their percolation thresholds, and discusses how correlations and clustering influence network topology.

Contribution

It presents two methods for creating correlated networks, generalizes existing algorithms, and explores the effects of correlations and clustering on network structure.

Findings

Percolation threshold calculated and validated through examples and simulations.

Correlations and clustering significantly impact network topology.

A model extension shows clustering coefficients independent of network size.

Abstract

A model of correlated random networks is examined, i.e. networks with correlations between the degrees of neighboring nodes. These nodes do not necessarily have to be direct neighbors, the maximum range of the correlations can be arbitrarily chosen. Two different methods for the creation of such networks are presented: one of them is a generalization of a well-known algorithm by Maslov and Sneppen. The percolation threshold for the model is calculated and the result is tested using analytically solvable examples and simulations. In the end the principal importance of correlations and clustering for the topology of networks is discussed. Using a straight-forward extension of the network model by Barabasi and Albert, it is shown how a clustering-coefficient independent of the network size can originate in growing networks.