Effect of degree correlations above the first shell on the percolation transition

TL;DR

This paper investigates how different algorithms for creating assortative networks affect percolation processes, revealing that network structure beyond Pearson's coefficient influences critical behavior.

Contribution

It introduces a generalized correlation measure at chemical distances and demonstrates that network generation algorithms impact percolation transitions.

Findings

Percolation behavior varies with the correlation algorithm used.

Inner network structures influence percolation observables.

Generalized Pearson's coefficient captures correlations beyond immediate neighbors.

Abstract

The use of degree-degree correlations to model realistic networks which are characterized by their Pearson's coefficient, has become widespread. However the effect on how different correlation algorithms produce different results on processes on top of them, has not yet been discussed. In this letter, using different correlation algorithms to generate assortative networks, we show that for very assortative networks the behavior of the main observables in percolation processes depends on the algorithm used to build the network. The different alghoritms used here introduce different inner structures that are missed in Pearson's coefficient. We explain the different behaviors through a generalization of Pearson's coefficient that allows to study the correlations at chemical distances l from a root node. We apply our findings to real networks.