A Markov Chain Approach to Randomly Grown Graphs
A Markov chain approach to the study of randomly grown graphs is proposed and applied to some popular models that have found use in biology and elsewhere. For most randomly grown graphs used in biology, it is not known whether the graph or properties of the graph converge (in some sense) as the numb...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2008-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2008/190836 |
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| _version_ | 1841524406552100864 |
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| author | Michael Knudsen Carsten Wiuf |
| author_facet | Michael Knudsen Carsten Wiuf |
| author_sort | Michael Knudsen |
| collection | DOAJ |
| description | A Markov chain approach to the study of randomly grown graphs is proposed and applied to some popular models that have found use in biology and elsewhere. For most randomly grown graphs used in biology, it is not known whether the graph or properties of the graph converge (in some sense) as the number of vertices becomes large. Particularly, we study the behaviour of the degree sequence, that is, the number of vertices with degree 0,1,…, in large graphs, and apply our results to the partial duplication model. We further illustrate the results by application to real data. |
| format | Article |
| id | doaj-art-9c8a27bc42dc49fb8f7ef2b5964c8f73 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2008-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-9c8a27bc42dc49fb8f7ef2b5964c8f732025-02-03T05:53:23ZengWileyJournal of Applied Mathematics1110-757X1687-00422008-01-01200810.1155/2008/190836190836A Markov Chain Approach to Randomly Grown GraphsMichael Knudsen0Carsten Wiuf1Bioinformatics Research Center, University of Aarhus, Høegh-Guldbergs Gade 10, Building 1090, Århus C 8000, DenmarkBioinformatics Research Center, University of Aarhus, Høegh-Guldbergs Gade 10, Building 1090, Århus C 8000, DenmarkA Markov chain approach to the study of randomly grown graphs is proposed and applied to some popular models that have found use in biology and elsewhere. For most randomly grown graphs used in biology, it is not known whether the graph or properties of the graph converge (in some sense) as the number of vertices becomes large. Particularly, we study the behaviour of the degree sequence, that is, the number of vertices with degree 0,1,…, in large graphs, and apply our results to the partial duplication model. We further illustrate the results by application to real data.http://dx.doi.org/10.1155/2008/190836 |
| spellingShingle | Michael Knudsen Carsten Wiuf A Markov Chain Approach to Randomly Grown Graphs Journal of Applied Mathematics |
| title | A Markov Chain Approach to Randomly Grown Graphs |
| title_full | A Markov Chain Approach to Randomly Grown Graphs |
| title_fullStr | A Markov Chain Approach to Randomly Grown Graphs |
| title_full_unstemmed | A Markov Chain Approach to Randomly Grown Graphs |
| title_short | A Markov Chain Approach to Randomly Grown Graphs |
| title_sort | markov chain approach to randomly grown graphs |
| url | http://dx.doi.org/10.1155/2008/190836 |
| work_keys_str_mv | AT michaelknudsen amarkovchainapproachtorandomlygrowngraphs AT carstenwiuf amarkovchainapproachtorandomlygrowngraphs AT michaelknudsen markovchainapproachtorandomlygrowngraphs AT carstenwiuf markovchainapproachtorandomlygrowngraphs |