Vertex Intrinsic Fitness: How to Produce Arbitrary Scale-Free Networks

TL;DR

This paper explores a vertex fitness-based model for generating scale-free networks, identifying conditions under which such networks naturally emerge, offering insights into their widespread occurrence and robustness.

Contribution

It introduces a flexible fitness-based model for scale-free network generation and derives general conditions for scale-free behavior to occur.

Findings

Scale-free networks can be generated under various fitness distributions and linking functions.

The model explains the ubiquity and robustness of scale-free structures.

Conditions for scale-free behavior are explicitly derived.

Abstract

We study a recent model of random networks based on the presence of an intrinsic character of the vertices called fitness. The vertices fitnesses are drawn from a given probability distribution density. The edges between pair of vertices are drawn according to a linking probability function depending on the fitnesses of the two vertices involved. We study here different choices for the probability distribution densities and the linking functions. We find that, irrespective of the particular choices, the generation of scale-free networks is straightforward. We then derive the general conditions under which scale-free behavior appears. This model could then represent a possible explanation for the ubiquity and robustness of such structures.