Discontinuous percolation via suppression of neighboring clusters in a network

TL;DR

This paper investigates a discontinuous percolation transition in bipartite networks where nodes rewire links to suppress neighboring clusters, leading to the formation of a giant component with finite size, supported by analytical insights.

Contribution

It introduces a model of bipartite networks with link rewiring that results in a discontinuous percolation transition, extending previous work on tree-like structures.

Findings

Discontinuous percolation transition observed with a giant component forming suddenly.

Critical behavior identified in the cluster size distribution.

Analytical explanation provided for the transition mechanism.

Abstract

Our recent study on the Bethe lattice reported that a discontinuous percolation transition emerges as the number of occupied links increases and each node rewires its links to locally suppress the growth of neighboring clusters. However, since the Bethe lattice is a tree, a macroscopic cluster forms as an infinite spanning tree but does not contain a finite fraction of the nodes. In this paper, we study a bipartite network that can be regarded as a locally tree-like structure with long-range neighbors. In this network, each node in one of the two partitions is allowed to rewire its links to nodes in the other partition to suppress the growth of neighboring clusters. We observe a discontinuous percolation transition characterized by the emergence of a single macroscopic cluster containing a finite fraction of nodes, followed by critical behavior of the cluster size distribution. We also provide an analytical explanation of the underlying mechanism.