Explosive percolation in thresholded networks

TL;DR

This paper demonstrates that explosive percolation, a sudden phase transition in network connectivity, can occur in thresholded networks generated from similarity matrices when edges are added in a specific sequence.

Contribution

It introduces a method to observe explosive percolation in realistic thresholded networks, expanding understanding beyond traditional random models.

Findings

Explosive percolation occurs in thresholded networks under certain edge addition schemes.

The order of edge addition critically influences the emergence of explosive percolation.

Thresholded networks can exhibit phase transitions similar to those in random network models.

Abstract

Explosive percolation in a network is a phase transition where a large portion of nodes becomes connected with an addition of a small number of edges. Although extensively studied in random network models and reconstructed real networks, explosive percolation has not been observed in a more realistic scenario where a network is generated by thresholding a similarity matrix describing between-node associations. In this report, I examine construction schemes of such thresholded networks, and demonstrate that explosive percolation can be observed by introducing edges in a particular order.