Evolving Scale-Free Network Model with Tunable Clustering

TL;DR

This paper introduces an extended scale-free network model incorporating local interactions and tunable clustering, providing analytical expressions for degree distribution and clustering coefficient that align well with numerical results.

Contribution

It presents a novel evolving network model with adjustable clustering, extending the BA model by including local world and edge addition mechanisms.

Findings

Degree distribution follows a power-law with exponent 3.

Clustering coefficient scales as k^{-1} plus a constant.

Analytical results match numerical simulations.

Abstract

The Barab\'{a}si-Albert (BA) model is extended to include the concept of local world and the microscopic event of adding edges. With probability $p$, we add a new node with $m$ edges which preferentially link to the nodes presented in the network; with probability $1-p$, we add $m$ edges among the present nodes. A node is preferentially selected by its degree to add an edge randomly among its neighbors. Using continuum theory and rate equation method we get the analytical expressions of the power-law degree distribution with exponent $\gamma=3$ and the clustering coefficient $c(k)\sim k^{-1}+c$. The analytical expressions are in good agreement with the numerical calculations.