Mutual selection in network evolution: the role of the intrinsic fitness

TL;DR

This paper introduces a model for network evolution based on intrinsic vertex fitness, leading to scale-free networks with power-law degree distributions, regardless of the fitness distribution.

Contribution

The authors propose a novel network growth mechanism incorporating vertex fitness and preferential attachment, resulting in generalized power-law networks.

Findings

Networks exhibit scale-free properties with power-law degree distributions.

The model's results are robust across different fitness distributions.

Preferential attachment based on fitness influences network topology.

Abstract

We propose a new mechanism leading to scale-free networks which is based on the presence of an intrinsic character of a vertex called fitness. In our model, a vertex $i$ is assigned a fitness $x_i$, drawn from a given probability distribution function $f(x)$. During network evolution, with rate $p$ we add a vertex $j$ of fitness $x_j$ and connect to an existing vertex $i$ of fitness $x_i$ selected preferentially to a linking probability function $g(x_i,x_j)$ which depends on the fitnesses of the two vertices involved and, with rate $1-p$ we create an edge between two already existed vertices with fitnesses $x_i$ and $x_j$, with a probability also preferential to the connection function $g(x_i,x_j)$. For the proper choice of $g$, the resulting networks have generalized power laws, irrespective of the fitness distribution of vertices.