The product representation of a locally dependent random graph

Kari Kuulasmaa

Research output: Contribution to journalArticle

Abstract

Directed graphs with random black and white colourings of edges such that the colours of edges from different vertices are mutually independent are called locally dependent random graphs. Two random graphs are equivalent if they cannot be distinguished from percolation processes on them if only the vertices are seen. A necessary and sufficient condition is given for when a locally dependent random graph is equivalent to a product random graph; that is one in which the edges can be grouped in such a way that within each group the colours of the edges are equivalent and between groups they are independent. As an application the random graph corresponding to a spatial general epidemic model is considered. © 1984.

Original languageEnglish
Pages (from-to)147-158
Number of pages12
JournalStochastic Processes and their Applications
Volume17
Issue number1
Publication statusPublished - May 1984

Keywords

  • Locally dependent random graph
  • percolation process spatial general epidemic

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