Scale-free networks with tunable degree distribution exponents

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 $k$, $P(p,k)\sim k^{-\gamma (p)}\mathcal{F}(k,p)$, where the function $\mathcal{F}$ 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.

12 pages, 2 figures, submitted to PRE

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Cited by in corpus (1)

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