Degree product rule tempers explosive percolation in the absence of global information

TL;DR

This paper introduces a local-information-based network growth model called the degree product rule process, which can delay percolation and reduce explosive transitions compared to global methods.

Contribution

It presents a new local-guided percolation model that interpolates between second and first order transitions and characterizes its critical behavior.

Findings

Second order phase transition with few candidate edges

First order transition in the global limit

Delays percolation and reduces explosiveness

Abstract

We introduce a guided network growth model, which we call the degree product rule process, that uses solely local information when adding new edges. For small numbers of candidate edges our process gives rise to a second order phase transition, but becomes first order in the limit of global choice. We provide the set of critical exponents required to characterize the nature of this percolation transition. Such a process permits interventions which can delay the onset of percolation while tempering the explosiveness caused by cluster product rule processes.