Crossover phenomena of percolation transition in evolution networks with hybrid attachment

TL;DR

This paper investigates how hybrid edge selection mechanisms influence the nature of percolation transitions in evolving networks, revealing crossover phenomena from discontinuous to continuous transitions depending on the selection bias.

Contribution

It introduces a tunable percolation model combining random and preferential attachment, demonstrating how transition types change with the selection strategy.

Findings

Discontinuous transition occurs with mostly random selection.

Multiple jumps in the largest component appear with degree-based selection.

Transition becomes continuous under fully preferential selection.

Abstract

A first-order percolation transition, called explosive percolation, was recently discovered in evolution networks with random edge selection under a certain restriction. However, the network percolation with more realistic evolution mechanisms such as preferential attachment has not yet been concerned. We propose a tunable network percolation model by introducing a hybrid mechanism of edge selection into the Bohman-Frieze-Wormald model, in which a parameter adjusts the relative weights between random and preferential selections. A large number of simulations indicate that there exist crossover phenomena of percolation transition by adjusting the parameter in the evolution processes. When the strategy of selecting a candidate edge is dominated by random selection, a single discontinuous percolation transition occurs. When a candidate edge is selected more preferentially based on node's degree, the size of the largest component undergoes multiple discontinuous jumps, which exhibits a peculiar difference from the network percolation of random selection with a certain restriction. Besides, the percolation transition becomes continuous when the candidate edge is selected completely preferentially.