TY - JOUR

T1 - Betweenness centrality of fractal and nonfractal scale-free model networks and tests on real networks

AU - Kitsak, Maksim

AU - Havlin, Shlomo

AU - Paul, Gerald

AU - Riccaboni, Massimo

AU - Pammolli, Fabio

AU - Stanley, H. Eugene

PY - 2007/5/31

Y1 - 2007/5/31

N2 - 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) ∼ C-δ. We find that for nonfractal scale-free networks δ=2, and for fractal scale-free networks δ=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 *, 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.

AB - 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) ∼ C-δ. We find that for nonfractal scale-free networks δ=2, and for fractal scale-free networks δ=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 *, 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.

UR - http://www.scopus.com/inward/record.url?scp=34547264299&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.75.056115

DO - 10.1103/PhysRevE.75.056115

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AN - SCOPUS:34547264299

SN - 1539-3755

VL - 75

JO - Physical Review E

JF - Physical Review E

IS - 5

M1 - 056115

ER -