A Random Growth Model with any Real or Theoretical Degree Distribution

TL;DR

This paper introduces a versatile random growth model capable of generating networks with nearly any desired degree distribution, including real-world and theoretical types, by inverting the recurrence relation for attachment functions.

Contribution

The paper presents a novel method to construct random network models with arbitrary degree distributions through an inverted recurrence approach, extending beyond traditional power-law assumptions.

Findings

The model successfully reproduces classical distributions like power-law, geometric, and Poisson.

It can fit real-world network degree distributions, such as Twitter.

Heavy-tailed distributions are linked to divergence in attachment functions.

Abstract

The degree distributions of complex networks are usually considered to be power law. However, it is not the case for a large number of them. We thus propose a new model able to build random growing networks with (almost) any wanted degree distribution. The degree distribution can either be theoretical or extracted from a real-world network. The main idea is to invert the recurrence equation commonly used to compute the degree distribution in order to find a convenient attachment function for node connections - commonly chosen as linear. We compute this attachment function for some classical distributions, as the power-law, broken power-law, geometric and Poisson distributions. We also use the model on an undirected version of the Twitter network, for which the degree distribution has an unusual shape. We finally show that the divergence of chosen attachment functions is heavily links to the heavy-tailed property of the obtained degree distributions.