Colouring, centrality and core-periphery structure in graphs
<p>Krivelevich and Patkós conjectured in 2009 that <em>χ(G(n, p)) ∼ χ=(G(n, p)) ∼ χ∗=(G(n, p))</em> for <em>C/n < p < 1 − ε,</em> where ε > 0. We prove this conjecture for <em>n−1+ε1 < p < 1 − ε2</em> where <em>ε1, ε2...
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| Formatua: | Thesis |
| Hizkuntza: | English |
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2013
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| Gaiak: |
| _version_ | 1826312348175958016 |
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| author | Rombach, M |
| author2 | Porter, MA |
| author_facet | Porter, MA Rombach, M |
| author_sort | Rombach, M |
| collection | OXFORD |
| description | <p>Krivelevich and Patkós conjectured in 2009 that <em>χ(G(n, p)) ∼ χ=(G(n, p)) ∼ χ∗=(G(n, p))</em> for <em>C/n < p < 1 − ε,</em> where ε > 0. We prove this conjecture for <em>n−1+ε1 < p < 1 − ε2</em> where <em>ε1, ε2 > 0</em>.</p> <p>We investigate several measures that have been proposed to indicate centrality of nodes in networks, and find examples of networks where they fail to distinguish any of the vertices nodes from one another. We develop a new method to investigate core-periphery structure, which entails identifying densely-connected core nodes and sparsely-connected periphery nodes.</p> <p>Finally, we present an experiment and an analysis of empirical networks, functional human brain networks. We found that reconfiguration patterns of dynamic communities can be used to classify nodes into a stiff core, a flexible periphery, and a bulk. The separation between this stiff core and flexible periphery changes as a person learns a simple motor skill and, importantly, it is a good predictor of how successful the person is at learning the skill. This temporally defined core-periphery organisation corresponds well with the core- periphery detected by the method that we proposed earlier the static networks created by averaging over the subjects dynamic functional brain networks.</p> |
| first_indexed | 2024-03-07T08:26:14Z |
| format | Thesis |
| id | oxford-uuid:7326ecc6-a447-474f-a03b-6ec244831ad4 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T08:26:14Z |
| publishDate | 2013 |
| record_format | dspace |
| spelling | oxford-uuid:7326ecc6-a447-474f-a03b-6ec244831ad42024-02-20T15:22:19ZColouring, centrality and core-periphery structure in graphsThesishttp://purl.org/coar/resource_type/c_db06uuid:7326ecc6-a447-474f-a03b-6ec244831ad4Statistical mechanics,structure of matter (mathematics)CombinatoricsMathematical biologyComputer science (mathematics)Information and communication,circuits (mathematics)Probability theory and stochastic processesEnglishOxford University Research Archive - Valet2013Rombach, MPorter, MAScott, AD<p>Krivelevich and Patkós conjectured in 2009 that <em>χ(G(n, p)) ∼ χ=(G(n, p)) ∼ χ∗=(G(n, p))</em> for <em>C/n < p < 1 − ε,</em> where ε > 0. We prove this conjecture for <em>n−1+ε1 < p < 1 − ε2</em> where <em>ε1, ε2 > 0</em>.</p> <p>We investigate several measures that have been proposed to indicate centrality of nodes in networks, and find examples of networks where they fail to distinguish any of the vertices nodes from one another. We develop a new method to investigate core-periphery structure, which entails identifying densely-connected core nodes and sparsely-connected periphery nodes.</p> <p>Finally, we present an experiment and an analysis of empirical networks, functional human brain networks. We found that reconfiguration patterns of dynamic communities can be used to classify nodes into a stiff core, a flexible periphery, and a bulk. The separation between this stiff core and flexible periphery changes as a person learns a simple motor skill and, importantly, it is a good predictor of how successful the person is at learning the skill. This temporally defined core-periphery organisation corresponds well with the core- periphery detected by the method that we proposed earlier the static networks created by averaging over the subjects dynamic functional brain networks.</p> |
| spellingShingle | Statistical mechanics,structure of matter (mathematics) Combinatorics Mathematical biology Computer science (mathematics) Information and communication,circuits (mathematics) Probability theory and stochastic processes Rombach, M Colouring, centrality and core-periphery structure in graphs |
| title | Colouring, centrality and core-periphery structure in graphs |
| title_full | Colouring, centrality and core-periphery structure in graphs |
| title_fullStr | Colouring, centrality and core-periphery structure in graphs |
| title_full_unstemmed | Colouring, centrality and core-periphery structure in graphs |
| title_short | Colouring, centrality and core-periphery structure in graphs |
| title_sort | colouring centrality and core periphery structure in graphs |
| topic | Statistical mechanics,structure of matter (mathematics) Combinatorics Mathematical biology Computer science (mathematics) Information and communication,circuits (mathematics) Probability theory and stochastic processes |
| work_keys_str_mv | AT rombachm colouringcentralityandcoreperipherystructureingraphs |