Discontinuous transition in explosive percolation via local suppression

TL;DR

This paper demonstrates that a discontinuous explosive percolation transition can occur through local suppression mechanisms involving finite rewiring, extending previous models that required global information.

Contribution

It introduces a model where local rewiring leads to a discontinuous transition, showing that global information is not necessary for explosive percolation.

Findings

Discontinuous transition occurs with finite rewiring nodes.

Local information suffices for explosive percolation.

Rewiring spreads outward from initial nodes.

Abstract

We study an explosive percolation model in which a link is randomly added and neighboring nodes sequentially rewire their links to suppress the growth of large clusters. In this manner, the rewiring nodes spread outward starting from the initial node closest to the added link. We show that a discontinuous transition emerges even when the total number of rewiring nodes after each link addition is finite. This finding implies that adding a link using the information of the cluster sizes attached to a finite set of link candidates (local information) can lead to a discontinuous transition if link rewiring is allowed. This result thus extends the previous result that a discontinuous transition arises only when a link is added using the information of the cluster sizes attached to an infinite number of link candidates (global information) in the absence of rewiring.