Breaking of the site-bond percolation universality in networks

TL;DR

This paper demonstrates that the critical exponents for bond and site percolation differ in certain networks, challenging the long-held belief of universality in percolation transitions.

Contribution

It provides the first analytical and numerical evidence of universality violation in percolation, specifically in networks with zero percolation thresholds like scale-free graphs.

Findings

Critical exponents differ between bond and site percolation in specific networks.

Universality assumption does not hold for networks with null percolation thresholds.

Implications for understanding real-world network robustness and phase transitions.

Abstract

The stochastic addition of either vertices or connections in a network leads to the observation of the percolation transition, a structural change with the appearance of a connected component encompassing a finite fraction of the system. Percolation has always been regarded as a substrate-dependent but model-independent process, in the sense that the critical exponents of the transition are determined by the geometry of the system, but they are identical for the bond and site percolation models. Here, we report a violation of such assumption. We provide analytical and numerical evidence of a difference in the values of the critical exponents between the bond and site percolation models in networks with null percolation thresholds, such as scale-free graphs with diverging second moment of the degree distribution. We discuss possible implications of our results in real networks, and provide additional insights on the anomalous nature of the percolation transition with null threshold.