Kitsak, Maksim and Havlin, Shlomo and Paul, Gerald and Riccaboni, Massimo and Pammolli, Fabio and Stanley, H. Eugene (2007): Betweenness Centrality of Fractal and NonFractal ScaleFree Model Networks and Tests on Real Networks. Published in: Physical Review E , Vol. 75, No. 5 (31 May 2007): 056115.

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Abstract
We study the betweenness centrality of fractal and nonfractal scalefree 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 scalefree networks have power law betweenness centrality distribution P(C) ~ C^δ. We find that for nonfractal scalefree networks δ = 2, and for fractal scalefree 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 AS 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.
Item Type:  MPRA Paper 

Original Title:  Betweenness Centrality of Fractal and NonFractal ScaleFree Model Networks and Tests on Real Networks 
Language:  English 
Keywords:  Interfirm networks; R&D collaborations, Pharmaceutical industry; ICT. 
Subjects:  L  Industrial Organization > L6  Industry Studies: Manufacturing > L65  Chemicals ; Rubber ; Drugs ; Biotechnology L  Industrial Organization > L2  Firm Objectives, Organization, and Behavior > L25  Firm Performance: Size, Diversification, and Scope O  Economic Development, Innovation, Technological Change, and Growth > O3  Innovation ; Research and Development ; Technological Change ; Intellectual Property Rights > O30  General E  Macroeconomics and Monetary Economics > E1  General Aggregative Models > E17  Forecasting and Simulation: Models and Applications L  Industrial Organization > L6  Industry Studies: Manufacturing > L60  General L  Industrial Organization > L0  General > L00  General L  Industrial Organization > L6  Industry Studies: Manufacturing > L63  Microelectronics ; Computers ; Communications Equipment 
Item ID:  15907 
Depositing User:  Laknori 
Date Deposited:  29 Jun 2009 14:49 
Last Modified:  10 Oct 2019 14:04 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/15907 