Farey graphs as models for complex networks
Farey sequences of irreducible fractions between 0 and 1 can be related to graph constructions known as Farey graphs. These graphs were first introduced by Matula and Kornerup in 1979 and further studied by Colbourn in 1982 and they have many interesting properties: they are minimally 3-colorable, u...
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2009 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/6094 |
| Acceso en línea: | https://hdl.handle.net/2117/6094 |
| Access Level: | acceso abierto |
| Palabra clave: | Graph theory Sequences (Mathematics) Operations research Farey graphs small-world graphs complex networks outerplanar Grafs, Teoria de Successions (Matemàtica) Investigació operativa Classificació AMS::11 Number theory::11B Sequences and sets Classificació AMS::05 Combinatorics::05C Graph theory Classificació AMS::90 Operations research, mathematical programming::90B Operations research and management science Àrees temàtiques de la UPC::Matemàtiques i estadística |
| Sumario: | Farey sequences of irreducible fractions between 0 and 1 can be related to graph constructions known as Farey graphs. These graphs were first introduced by Matula and Kornerup in 1979 and further studied by Colbourn in 1982 and they have many interesting properties: they are minimally 3-colorable, uniquely Hamiltonian, maximally outerplanar and perfect. In this paper we introduce a simple generation method for a Farey graph family, and we study analytically relevant topological properties: order, size, degree distribution and correlation, clustering, transitivity, diameter and average distance. We show that the graphs are a good model for networks associated with some complex systems. |
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