eprintid: 643
rev_number: 18
eprint_status: archive
userid: 2
dir: disk0/00/00/06/43
datestamp: 2011-06-30 14:26:40
lastmod: 2014-12-18 15:44:51
status_changed: 2011-06-30 14:26:40
type: article
metadata_visibility: show
item_issues_count: 0
creators_name: Kitsak, Maksim
creators_name: Havlin, Shlomo
creators_name: Paul, Gerald
creators_name: Riccaboni, Massimo
creators_name: Pammolli, Fabio
creators_name: Stanley, H. Eugene
creators_id: 
creators_id: 
creators_id: 
creators_id: massimo.riccaboni@imtlucca.it
creators_id: f.pammolli@imtlucca.it
creators_id: 
title: Betweenness centrality of fractal and nonfractal scale-free model networks and tests on real networks
ispublished: pub
subjects: QC
divisions: EIC
full_text_status: public
keywords: PACS: 89.75.Hc

note: © 2007 The American Physical Society
abstract: 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 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.
date: 2007-05
date_type: published
publication: Physical Review E
volume: 75
number: 5
publisher: American Physical Society
pagerange: 056115
id_number: 10.1103/PhysRevE.75.056115
refereed: TRUE
issn: 1539-3755
official_url: http://link.aps.org/doi/10.1103/PhysRevE.75.056115
citation:   Kitsak, Maksim and Havlin, Shlomo and Paul, Gerald and Riccaboni, Massimo and Pammolli, Fabio and Stanley, H. Eugene  Betweenness centrality of fractal and nonfractal scale-free model networks and tests on real networks.  Physical Review E, 75 (5).  056115.  ISSN 1539-3755      (2007)  
document_url: http://eprints.imtlucca.it/643/1/betweenness_2007a.pdf
document_url: http://eprints.imtlucca.it/643/4/PhysRevE.Riccaboni_Pammolli_2007.pdf