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A Markov Chain Approach to Randomly Grown Graphs

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Listed:
  • Michael Knudsen
  • Carsten Wiuf

Abstract

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.

Suggested Citation

  • Michael Knudsen & Carsten Wiuf, 2008. "A Markov Chain Approach to Randomly Grown Graphs," Journal of Applied Mathematics, John Wiley & Sons, vol. 2008(1).
    • Handle: RePEc:wly:jnljam:v:2008:y:2008:i:1:n:190836
    DOI: 10.1155/2008/190836
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    References listed on IDEAS

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