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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2112.03535 |
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| _version_ | 1866914125083312128 |
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| author | Chatterji, Indira Lawson, Austin |
| author_facet | Chatterji, Indira Lawson, Austin |
| contents | Expanders are sparse graph that are strongly connected, where {\it connectivity} is quantified using eigenvalues of the adjacency matrix, and {\it sparsity} in terms of vertex valency. We give a model of random graphs and study their connectivity and sparsity. This model is a particular case of soft geometric random graphs, and allows to construct sparse graphs with good expansion properties, as well as highly clustered ones. On those graphs, we study the speed at which random walks spread in the graph, and visit all vertices. As an illustration, we build a model for mainland France and study the spread of random walks under several types of lockdown. Our experiments show that completely closing medium and long distance travel to slow down the spread of a random walk is more efficient than than local restrictions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_03535 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Horospherical random graphs and lockdown strategies Chatterji, Indira Lawson, Austin Combinatorics Metric Geometry 60-04, 91-05 Expanders are sparse graph that are strongly connected, where {\it connectivity} is quantified using eigenvalues of the adjacency matrix, and {\it sparsity} in terms of vertex valency. We give a model of random graphs and study their connectivity and sparsity. This model is a particular case of soft geometric random graphs, and allows to construct sparse graphs with good expansion properties, as well as highly clustered ones. On those graphs, we study the speed at which random walks spread in the graph, and visit all vertices. As an illustration, we build a model for mainland France and study the spread of random walks under several types of lockdown. Our experiments show that completely closing medium and long distance travel to slow down the spread of a random walk is more efficient than than local restrictions. |
| title | Horospherical random graphs and lockdown strategies |
| topic | Combinatorics Metric Geometry 60-04, 91-05 |
| url | https://arxiv.org/abs/2112.03535 |