Scale-free properties of weighted networks with connectivity-driven topology

TL;DR

This paper investigates the scale-free properties of weighted networks with topology driven by node connectivity, demonstrating that certain modifications to attachment rules preserve degree and weight distributions while speeding up simulations.

Contribution

It introduces a modified attachment rule based on degree ratios that maintains scale-free distributions and enhances simulation efficiency in evolving weighted networks.

Findings

Degree and weight distributions remain unchanged under the modified attachment rule.

The rate equations have solutions showing power-law behavior for large weights.

Modification accelerates numerical simulations of weighted networks.

Abstract

The rate equations are used to study the scale-free behavior of the weight distribution in evolving networks whose topology is determined only by degrees of preexisting vertices. An analysis of these equations shows that the degree distribution and thereby the weight distribution remain unchanged when the probability rate of attaching new nodes is replaced with some unnormalized rate determined by the ratio of the degree of a randomly selected old node to the maximal node degree at the current stage of the network evolution. Such a modification of the attachment rule is argued to accelerate considerably numerical simulations of both unweighted and weighted networks belonging to the class of investigated evolving systemes. It is also proved that the studied rate equations have a solution corresponding to the total (concentrated at individual vertices) distribution displaying the power-law behavior for asymptotically large weights.