Criticality and Continuity of Explosive Site Percolation in Random Networks

TL;DR

This paper investigates the critical behavior and discontinuity of explosive site percolation in Erdős-Rényi networks, revealing how the percolation threshold scales with network degree and conditions for discontinuous transitions.

Contribution

It introduces a best-of-m rule for explosive percolation and analyzes the critical point and discontinuity, extending understanding of network robustness and percolation phenomena.

Findings

Critical percolation point scales with average degree.

Discontinuous percolation occurs only if the parameter approaches infinity.

Results generalize ordinary percolation and offer new insights into network robustness.

Abstract

This Letter studies the critical point as well as the discontinuity of a class of explosive site percolation in Erd\"{o}s and R\'{e}nyi (ER) random network. The class of the percolation is implemented by introducing a best-of-m rule. Two major results are found: i). For any specific $m$, the critical percolation point scales with the average degree of the network while its exponent associated with $m$ is bounded by -1 and $\sim-0.5$. ii). Discontinuous percolation could occur on sparse networks if and only if $m$ approaches infinite. These results not only generalize some conclusions of ordinary percolation but also provide new insights to the network robustness.