Neighbor-induced damage percolation

TL;DR

This paper provides an exact analytical solution for neighbor-induced damage percolation in uncorrelated random graphs, revealing critical thresholds, phase transitions, and the impact of network heterogeneity and topology on system robustness.

Contribution

It introduces a precise solution for the size of giant components in neighbor-induced damage percolation, including new insights into phase transitions and critical exponents in various network types.

Findings

Giant usable component appears at a finite threshold regardless of heterogeneity.

Network robustness is maximized at a finite optimal average degree.

A damaged phase with a giant damaged component exists at high connectivity, with phase transitions characterized by standard or new critical exponents.

Abstract

We consider neighbor-induced damage percolation, a model describing systems where the inactivation of some elements may damage their neighboring active ones, making them unusable. We present an exact solution for the size of the giant usable component (GUC) and the giant damaged component (GDC) in uncorrelated random graphs. We show that, even for strongly heterogeneous distributions, the GUC always appears at a finite threshold and its formation is characterized by homogeneous mean-field percolation critical exponents. The threshold is a nonmonotonic function of connectivity: robustness is maximized by networks with finite optimal average degree. We also show that, if the average degree is large enough, a damaged phase appears, characterized by the existence of a GDC, bounded by two distinct percolation transitions. The birth and the dismantling of the GDC are characterized by standard percolation critical exponents in networks, except for the dismantling in scale-free networks where new critical exponents are found. Numerical simulations on regular lattices in D = 2 show that the existence of a GDC depends not only on the spatial dimension but also on the lattice coordination number.