dorsal/arxiv
View SchemaTwo complementary representations of a scale-free network
| Authors | J. C. Nacher, T. Yamada, S. Goto, M. Kanehisa, T. Akutsu |
|---|---|
| Categories | |
| ArXiv ID | physics/0402072 |
| URL | https://arxiv.org/abs/physics/0402072 |
| DOI | 10.1016/j.physa.2004.09.013 |
| Journal | Physica A 349 (2005) 349-363 |
Abstract
Several studies on real complex networks from different fields as biology, economy, or sociology have shown that the degree of nodes (number of edges connected to each node) follows a scale-free power-law distribution like $P(k)\approx k^{-\gamma}$, where $P(k)$ denotes the frequency of the nodes that are connected to $k$ other nodes. Here we have carried out a study on scale-free networks, where a line graph transformation (i.e., edges in an initial network are transformed into nodes) is applied to a power-law distribution. Our results indicate that a power-law distribution as $P(k)\approx k^{-\gamma +1}$ is found for the transformed network together with a peak for low-degree nodes. In the present work we show a parametrization of this behaviour and discuss its application to real networks as metabolic networks, protein-protein interaction network and World Wide Web.
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"abstract": "Several studies on real complex networks from different fields as biology,\neconomy, or sociology have shown that the degree of nodes (number of edges\nconnected to each node) follows a scale-free power-law distribution like\n$P(k)\\approx k^{-\\gamma}$, where $P(k)$ denotes the frequency of the nodes that\nare connected to $k$ other nodes. Here we have carried out a study on\nscale-free networks, where a line graph transformation (i.e., edges in an\ninitial network are transformed into nodes) is applied to a power-law\ndistribution. Our results indicate that a power-law distribution as\n$P(k)\\approx k^{-\\gamma +1}$ is found for the transformed network together with\na peak for low-degree nodes. In the present work we show a parametrization of\nthis behaviour and discuss its application to real networks as metabolic\nnetworks, protein-protein interaction network and World Wide Web.",
"arxiv_id": "physics/0402072",
"authors": [
"J. C. Nacher",
"T. Yamada",
"S. Goto",
"M. Kanehisa",
"T. Akutsu"
],
"categories": [
"physics.bio-ph",
"cond-mat.dis-nn",
"cond-mat.stat-mech",
"physics.data-an"
],
"doi": "10.1016/j.physa.2004.09.013",
"journal_ref": "Physica A 349 (2005) 349-363",
"title": "Two complementary representations of a scale-free network",
"url": "https://arxiv.org/abs/physics/0402072"
},
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