Weighted Scale-Free Networks with Stochastic Weight Assignments

TL;DR

This paper introduces a stochastic weighted scale-free network model where link weights depend on node popularity and fitness, showing how the total weight distribution follows a power law with an exponent influenced by the probability parameter.

Contribution

The study presents a novel stochastic scheme for weight assignment in scale-free networks, deriving an analytical expression and exploring the effects of fitness-dependent link formation.

Findings

Total weight distribution follows a power law with a variable exponent.

Exponent decreases as the probability of weight driven by connectivity increases.

Analytical expression explains the observed numerical results.

Abstract

We propose and study a model of weighted scale-free networks incorporating a stochastic scheme for weight assignments to the links, taking into account both the popularity and fitness of a node. As the network grows the weights of links are driven either by the connectivity with probability $p$ or by the fitness with probability $1-p$. Results of numerical simulations show that the total weight associated with a selected node exhibits a power law distribution with an exponent $\sigma$, the value of which depends on the probability $p$. The exponent $\sigma$ decreases continuously as $p$ increases. For $p=0$, the total weight distribution displays the same scaling behavior as that of the connectivity distribution with $\sigma= \gamma = 3$, where $\gamma$ is the exponent characterizing the connectivity distribution. An analytical expression for the total weight is derived so as to explain the features observed in the numerical results. Numerical results are also presented for a generalized model with a fitness-dependent link formation mechanism.