dorsal/arxiv
View SchemaNeighborhood properties of complex networks
| Authors | R. F. S. Andrade, J. G. V. Miranda, Thierry Petit Lobao |
|---|---|
| Categories | |
| ArXiv ID | physics/0508068 |
| URL | https://arxiv.org/abs/physics/0508068 |
| DOI | 10.1103/PhysRevE.73.046101 |
Abstract
A concept of neighborhood in complex networks is addressed based on the criterion of the minimal number os steps to reach other vertices. This amounts to, starting from a given network $R_1$, generating a family of networks $R_\ell, \ell=2,3,...$ such that, the vertices that are $\ell$ steps apart in the original $R_1$, are only 1 step apart in $R_\ell$. The higher order networks are generated using Boolean operations among the adjacency matrices $M_\ell$ that represent $R_\ell$. The families originated by the well known linear and the Erd\"os-Renyi networks are found to be invariant, in the sense that the spectra of $M_\ell$ are the same, up to finite size effects. A further family originated from small world network is identified.
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"abstract": "A concept of neighborhood in complex networks is addressed based on the\ncriterion of the minimal number os steps to reach other vertices. This amounts\nto, starting from a given network $R_1$, generating a family of networks\n$R_\\ell, \\ell=2,3,...$ such that, the vertices that are $\\ell$ steps apart in\nthe original $R_1$, are only 1 step apart in $R_\\ell$. The higher order\nnetworks are generated using Boolean operations among the adjacency matrices\n$M_\\ell$ that represent $R_\\ell$. The families originated by the well known\nlinear and the Erd\\\"os-Renyi networks are found to be invariant, in the sense\nthat the spectra of $M_\\ell$ are the same, up to finite size effects. A further\nfamily originated from small world network is identified.",
"arxiv_id": "physics/0508068",
"authors": [
"R. F. S. Andrade",
"J. G. V. Miranda",
"Thierry Petit Lobao"
],
"categories": [
"physics.data-an",
"physics.comp-ph"
],
"doi": "10.1103/PhysRevE.73.046101",
"title": "Neighborhood properties of complex networks",
"url": "https://arxiv.org/abs/physics/0508068"
},
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