Suppression effect on explosive percolations

TL;DR

This paper investigates how suppression mechanisms in network growth models influence the nature of percolation transitions, revealing that suppression can lead to either continuous or explosive, discontinuous transitions depending on the dynamic rules applied.

Contribution

It demonstrates that the type of percolation transition depends on the specific dynamic rules governing cluster growth, clarifying the conditions for explosive versus continuous transitions.

Findings

Suppression can induce explosive percolation.

The nature of the transition depends on dynamic rules.

Suppressed growth can lead to discontinuous transitions.

Abstract

When a group of people unknown to each other meet and familiarize among themselves, over time they form a community on a macroscopic scale. This phenomenon can be understood in the context of percolation transition (PT) of networks, which takes place continuously in the classical random graph model. Recently, a modified model was introduced in which the formation of the community was suppressed. Then the PT occurs explosively at a delayed transition time. Whether the explosive PT is indeed discontinuous or continuous becomes controversial. Here we show that type of PT depends on a detailed dynamic rule. Thus, when the dynamic rule is designed to suppress the growth of overall clusters, then the explosive PT could be discontinuous.