Dynamic scaling, data-collapse and self-similarity in Barabási-Albert networks

Abstract

In this article, we show that if each node of the Barabási-Albert (BA) network is characterized by the generalized degree $q$, i.e. the product of their degree $k$ and the square root of their respective birth time, then the distribution function $F(q,t)$ exhibits dynamic scaling $F(q,t\to \infty )\sim t^{-1/2}\varphi (q/t^{1/2})$ where $\varphi (x)$ is the scaling function. We verified it by showing that a series of distinct $F(q,t)$ vs $q$ curves for different network sizes $N$ collapse onto a single universal curve if we plot $t^{1/2}F(q,t)$ vs $q/t^{1/2}$ instead. Finally, we show that the BA network falls into two universality classes depending on whether new nodes arrive with single edge ($m=1$) or with multiple edges ($m>1$).

5 pages, six figures, Minor changes in the title, abstract, figures and in the text in response to referee reports

References in corpus (6)

• The structure and function of complex networks
• Scale-free brain functional networks
• Structural Vulnerability of the North American Power Grid
• Preferential attachment in the protein network evolution
• Scale-free network topology and multifractality in weighted planar stochastic lattice
• Finite size effects in Barabasi-Albert growing networks

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