### 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 language | English |
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Pages (from-to) | 147-158 |

Number of pages | 12 |

Journal | Stochastic Processes and their Applications |

Volume | 17 |

Issue number | 1 |

Publication status | Published - May 1984 |

### Keywords

- Locally dependent random graph
- percolation process spatial general epidemic

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## Cite this

*Stochastic Processes and their Applications*,

*17*(1), 147-158.