Emergence of Clusters in Growing Networks with Aging

TL;DR

This paper investigates a model of growing networks with aging effects, revealing a first-order phase transition leading to a giant cluster and a topological change from tree-like to linear structures, with implications for network universality classes.

Contribution

It introduces a novel model incorporating node aging in network growth and characterizes the resulting phase transition and topological changes through simulations and scaling analysis.

Findings

Giant cluster emerges at a first-order transition.

Transition belongs to the universality class of 1D percolation.

Topological shift from tree-like to quasi-linear structure.

Abstract

We study numerically a model of nonequilibrium networks where nodes and links are added at each time step with aging of nodes and connectivity- and age-dependent attachment of links. By varying the effects of age in the attachment probability we find, with numerical simulations and scaling arguments, that a giant cluster emerges at a first-order critical point and that the problem is in the universality class of one dimensional percolation. This transition is followed by a change in the giant cluster's topology from tree-like to quasi-linear, as inferred from measurements of the average shortest-path length, which scales logarithmically with system size in one phase and linearly in the other.