Scale-free networks with tunable degree distribution exponents

TL;DR

This paper introduces a hybrid model for scale-free networks with a tunable degree distribution exponent, combining popularity-driven and fitness-driven attachment mechanisms, and derives an explicit degree distribution formula.

Contribution

The study presents a new model of scale-free networks with a tunable exponent, integrating two attachment mechanisms and deriving an explicit degree distribution.

Findings

Degree distribution follows a power-law with a tunable exponent.

Analytical results agree with numerical simulations.

Degree distribution behavior varies with the parameter p.

Abstract

We propose and study a model of scale-free growing networks that gives a degree distribution dominated by a power-law behavior with a model-dependent, hence tunable, exponent. The model represents a hybrid of the growing networks based on popularity-driven and fitness-driven preferential attachments. As the network grows, a newly added node establishes $m$ new links to existing nodes with a probability $p$ based on popularity of the existing nodes and a probability $1-p$ based on fitness of the existing nodes. An explicit form of the degree distribution $P(p,k)$ is derived within a mean field approach. For reasonably large $k$, $P(p,k) \sim k^{-\gamma(p)}{\cal F}(k,p)$, where the function ${\cal F}$ is dominated by the behavior of $1/\ln(k/m)$ for small values of $p$ and becomes $k$-independent as $p \to 1$, and $\gamma(p)$ is a model-dependent exponent. The degree distribution and the exponent $\gamma(p)$ are found to be in good agreement with results obtained by extensive numerical simulations.