Weight-driven growing networks

TL;DR

This paper investigates weight-driven growing networks where link weights influence attachment probability, revealing a universal node weight distribution with a tail decay of w^-3, independent of link weight distribution.

Contribution

It introduces a model of growing networks driven by link weights and derives a universal node weight distribution tail, independent of link weight distribution.

Findings

Node weight distribution follows a universal w^-3 tail.

Results are exact for exponential link weight distribution.

Distribution is algebraic over the entire weight range for certain cases.

Abstract

We study growing networks in which each link carries a certain weight (randomly assigned at birth and fixed thereafter). The weight of a node is defined as the sum of the weights of the links attached to the node, and the network grows via the simplest weight-driven rule: A newly-added node is connected to an already existing node with the probability which is proportional to the weight of that node. We show that the node weight distribution n(w) has a universal, that is independent on the link weight distribution, tail: n(w) ~ w^-3 as w->oo. Results are particularly neat for the exponential link weight distribution when n(w) is algebraic over the entire weight range.