2011/01/31 by M. K. Hassan, M. Kamrul Hassan, M. Z. Hassan +3
Computer Science · Mathematics · Physics and Astronomy · #Combinatorics #Complex Network Analysis Techniques #Condensed matter physics #Degree (music) #Exponent #Function (biology) #Geometry #Graph theory and applications #Mathematical physics #Mathematics #Physics #Scaling #Series (stratigraphy) #Stochastic processes and statistical mechanics #Universality (dynamical systems) #cond-mat.dis-nn #cond-mat.stat-mech #cs.SI #physics.soc-ph
paper · pdf · doi:10.1088/1751-8113/44/17/175101
published as J. Phys. A: Math. Theor. 44, 175101 (2011) · 5 pages, six figures, Minor changes in the title, abstract, figures and in the text in response to referee reports
openalex publication_date 2011/04/04 · arxiv created 2011/04/07 · arxiv updated 2015/03/18 · openalex created_date 2020/11/23 · openalex updated_date 2026/08/05
In this paper, 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 → ∞ ) ∼ t −1/2 ϕ( q / t 1/2 ) where ϕ( 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).