Discontinuous percolation via suppression of neighboring clusters in a network.

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 treelike 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.