@article{eprints643,
           pages = {056115},
          number = {5},
           month = {May},
          volume = {75},
            year = {2007},
           title = {Betweenness centrality of fractal and nonfractal scale-free model networks and tests on real networks},
          author = {Maksim Kitsak and Shlomo Havlin and Gerald Paul and Massimo Riccaboni and Fabio Pammolli and H. Eugene Stanley},
       publisher = {American Physical Society},
         journal = {Physical Review E},
            note = {{\copyright} 2007 The American Physical Society},
        keywords = {PACS: 89.75.Hc
},
        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){$\sim$}C?{\ensuremath{\delta}}. We find that for nonfractal scale-free networks {\ensuremath{\delta}}=2, and for fractal scale-free networks {\ensuremath{\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 ?*, 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.},
             url = {http://eprints.imtlucca.it/643/}
}