Revisiting finite size effect of percolation in degree correlated networks

TL;DR

This paper examines bond percolation in degree-correlated networks with Poisson degree distribution, revealing that despite finite-size effects, the critical behavior aligns with mean-field theory regardless of correlation strength.

Contribution

It clarifies the finite-size effects and confirms that the critical behavior in degree-correlated networks follows mean-field predictions.

Findings

Finite-size effects are significant with strong degree correlations.

Critical exponents indicate mean-field behavior.

Degree correlations do not alter the universality class.

Abstract

In this study, we investigate bond percolation in networks that have the Poisson degree distribution and a nearest-neighbor degree-degree correlation. Previous numerical studies on percolation critical behaviors of degree-correlated networks remain controversial. We perform finite-size scaling for the peak values of the second-largest cluster size and the mean cluster size and find a large finite-size effect when a network has a strong degree-degree correlation. Evaluating the size dependence of estimated critical exponents carefully, we demonstrate that the bond percolation in the networks exhibits the mean-field critical behavior, independent of the strength of their nearest-neighbor degree correlations.