2007/02/19 by Maksim Kitsak, Shlomo Havlin, Gerald Paul +3
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Betweenness centrality #Bioinformatics and Genomic Networks #Centrality #Combinatorics #Complex Network Analysis Techniques #Complex network #Degree distribution #Fractal #Fractal dimension #Geometry #Mathematical analysis #Mathematics #Opinion Dynamics and Social Influence #Physics #Scale-free network #Scaling #Statistical physics #Topology (electrical circuits) #physics.data-an #physics.soc-ph
paper · pdf · doi:10.1103/physreve.75.056115
19 pages, 6 figures. Submitted to PRE
arxiv created 2007/02/19 · openalex publication_date 2007/05/31 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study the betweenness centrality of fractal and nonfractal scale-free network models as well as real networks. We show that the correlation between degree and betweenness centrality C of nodes is much weaker in fractal network models compared to nonfractal models. We also show that nodes of both fractal and nonfractal scale-free networks have power-law betweenness centrality distribution P(C) approximately C(-delta). We find that for nonfractal scale-free networks delta=2, and for fractal scale-free networks delta=2-1/dB, where dB is the dimension of the fractal network. We support these results by explicit calculations on four real networks: pharmaceutical firms (N=6776), yeast (N=1458), WWW (N=2526), and a sample of Internet network at the autonomous system level (N=20566), where N is the number of nodes in the largest connected component of a network. We also study the crossover phenomenon from fractal to nonfractal networks upon adding random edges to a fractal network. We show that the crossover length l*, separating fractal and nonfractal regimes, scales with dimension dB of the network as p(-1/dB), where p is the density of random edges added to the network. We find that the correlation between degree and betweenness centrality increases with p.