A general geometric growth model for pseudofractal scale-free web

TL;DR

This paper introduces a flexible geometric growth model for pseudofractal scale-free networks, capturing key properties like degree distribution, clustering, and small-world characteristics through tunable parameters.

Contribution

It provides an exact analytical framework for a general class of pseudofractal scale-free networks with adjustable degree exponents and clustering.

Findings

Networks are disassortative and follow power-law degree distributions.

Clustering coefficient inversely proportional to node degree.

Diameter grows logarithmically with network size.

Abstract

We propose a general geometric growth model for pseudofractal scale-free web, which is controlled by two tunable parameters. We derive exactly the main characteristics of the networks: degree distribution, second moment of degree distribution, degree correlations, distribution of clustering coefficient, as well as the diameter, which are partially determined by the parameters. Analytical results show that the resulting networks are disassortative and follow power-law degree distributions, with a more general degree exponent tuned from 2 to $1+\frac{\ln3}{\ln2}$; the clustering coefficient of each individual node is inversely proportional to its degree and the average clustering coefficient of all nodes approaches to a large nonzero value in the infinite network order; the diameter grows logarithmically with the number of network nodes. All these reveal that the networks described by our model have small-world effect and scale-free topology.