Dynamic scaling, datacollapse and selfsimilarity in BarabásiAlbert networks
Abstract
In this paper, we show that if each node of the BarabásiAlbert (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 → ∞) ~ t^{1/2}phi(q/t^{1/2}) where phi(x) is the scaling function. We verified it by showing that a series of distinct F(q, t) versus q curves for different network sizes N collapse onto a single universal curve if we plot t^{1/2}F(q, t) versus 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).
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 April 2011
 DOI:
 10.1088/17518113/44/17/175101
 arXiv:
 arXiv:1101.4730
 Bibcode:
 2011JPhA...44q5101K
 Keywords:

 Condensed Matter  Statistical Mechanics;
 Condensed Matter  Disordered Systems and Neural Networks;
 Computer Science  Social and Information Networks;
 Physics  Physics and Society
 EPrint:
 5 pages, six figures, Minor changes in the title, abstract, figures and in the text in response to referee reports