dorsal/arxiv
View SchemaBetweenness Centrality of Fractal and Non-Fractal Scale-Free Model Networks and Tests on Real Networks
| Authors | Maksim Kitsak, Shlomo Havlin, Gerald Paul, Massimo Riccaboni, Fabio Pammolli, H. Eugene Stanley |
|---|---|
| Categories | |
| ArXiv ID | physics/0702001 |
| URL | https://arxiv.org/abs/physics/0702001 |
| DOI | 10.1103/PhysRevE.75.056115 |
Abstract
We study the betweenness centrality of fractal and non-fractal 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 non-fractal models. We also show that nodes of both fractal and non-fractal scale-free networks have power law betweenness centrality distribution $P(C)\sim C^{-\delta}$. We find that for non-fractal scale-free networks $\delta = 2$, and for fractal scale-free networks $\delta = 2-1/d_{B}$, where $d_{B}$ 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 non-fractal networks upon adding random edges to a fractal network. We show that the crossover length $\ell^{*}$, separating fractal and non-fractal regimes, scales with dimension $d_{B}$ of the network as $p^{-1/d_{B}}$, where $p$ is the density of random edges added to the network. We find that the correlation between degree and betweenness centrality increases with $p$.
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"abstract": "We study the betweenness centrality of fractal and non-fractal scale-free\nnetwork models as well as real networks. We show that the correlation between\ndegree and betweenness centrality $C$ of nodes is much weaker in fractal\nnetwork models compared to non-fractal models. We also show that nodes of both\nfractal and non-fractal scale-free networks have power law betweenness\ncentrality distribution $P(C)\\sim C^{-\\delta}$. We find that for non-fractal\nscale-free networks $\\delta = 2$, and for fractal scale-free networks $\\delta =\n2-1/d_{B}$, where $d_{B}$ is the dimension of the fractal network. We support\nthese results by explicit calculations on four real networks: pharmaceutical\nfirms (N=6776), yeast (N=1458), WWW (N=2526), and a sample of Internet network\nat AS level (N=20566), where $N$ is the number of nodes in the largest\nconnected component of a network. We also study the crossover phenomenon from\nfractal to non-fractal networks upon adding random edges to a fractal network.\nWe show that the crossover length $\\ell^{*}$, separating fractal and\nnon-fractal regimes, scales with dimension $d_{B}$ of the network as\n$p^{-1/d_{B}}$, where $p$ is the density of random edges added to the network.\nWe find that the correlation between degree and betweenness centrality\nincreases with $p$.",
"arxiv_id": "physics/0702001",
"authors": [
"Maksim Kitsak",
"Shlomo Havlin",
"Gerald Paul",
"Massimo Riccaboni",
"Fabio Pammolli",
"H. Eugene Stanley"
],
"categories": [
"physics.soc-ph",
"physics.data-an"
],
"doi": "10.1103/PhysRevE.75.056115",
"title": "Betweenness Centrality of Fractal and Non-Fractal Scale-Free Model Networks and Tests on Real Networks",
"url": "https://arxiv.org/abs/physics/0702001"
},
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