Percolation on dense random graphs with given degrees
In this paper, we study the order of the largest connected component of a random graph having two sources of randomness: first, the graph is chosen randomly from all graphs with a given degree sequence, and then bond percolation is applied. Far from being able to classify all such degree sequences,...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2024 |
| 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:2117/409535 |
| Acceso en línea: | https://hdl.handle.net/2117/409535 https://dx.doi.org/10.1016/j.jctb.2024.03.002 |
| Access Level: | acceso abierto |
| Palabra clave: | Graph theory Statistical mechanics Percolation Degree sequence Giant component Threshold Switching method Grafs, Teoria de Mecànica estadística Classificació AMS::05 Combinatorics::05C Graph theory Classificació AMS::82 Statistical mechanics, structure of matter::82C Time-dependent statistical mechanics (dynamic and nonequilibrium) Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs Àrees temàtiques de la UPC::Matemàtiques i estadística::Estadística matemàtica |
| Sumario: | In this paper, we study the order of the largest connected component of a random graph having two sources of randomness: first, the graph is chosen randomly from all graphs with a given degree sequence, and then bond percolation is applied. Far from being able to classify all such degree sequences, we exhibit several new threshold phenomena for the order of the largest component in terms of both sources of randomness. We also provide an example of a degree sequence for which the order of the largest component undergoes an unbounded number of jumps in terms of the percolation parameter, giving rise to a behavior that cannot be observed without percolation. |
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