Construction and Analysis of Random Networks with Explosive Percolation

TL;DR

This paper investigates the mechanisms behind explosive phase transitions in random networks, providing tools to predict such transitions and introducing new models that exhibit these phenomena.

Contribution

It uncovers the underlying mechanism of explosive percolation and develops predictive tools, along with proposing new models demonstrating explosive transitions.

Findings

Identified the mechanism behind explosive phase transitions.

Developed tools to predict explosive transitions in networks.

Presented new models with explosive percolation behavior.

Abstract

The existence of explosive phase transitions in random (Erd\H os R\'enyi-type) networks has been recently documented by Achlioptas et al.\ [Science {\bf 323}, 1453 (2009)] via simulations. In this Letter we describe the underlying mechanism behind these first-order phase transitions and develop tools that allow us to identify (and predict) when a random network will exhibit an explosive transition. Several interesting new models displaying explosive transitions are also presented.