### Abstract

Under the unifying umbrella of a general result of Penrose & Yukich [Ann. Appl. Probab., (2003) 13, 277--303] we give laws of large numbers (in the Lp sense) for the total power-weighted length of several nearest-neighbour type graphs on random point sets in Rd, d in N. Some of these results are known; some are new. We give limiting constants explicitly, where previously they have been evaluated in less generality or not at all. The graphs we consider include the k-nearest neighbours graph, the Gabriel graph, the minimal directed spanning forest, and the on-line nearest-neighbour graph.

Original language | English |
---|---|

Pages (from-to) | 326-342 |

Number of pages | 17 |

Journal | Advances in Applied Probability |

Volume | 39 |

Issue number | 2 |

DOIs | |

Publication status | Published - Jun 2007 |

### Keywords

- nearest-neighbour-type graph
- law of large numbers
- spanning forest
- spatial network evolution
- explicit laws
- large numbers
- random

## Fingerprint Dive into the research topics of 'Explicit laws of large numbers for random nearest-neighbour-type graphs'. Together they form a unique fingerprint.

## Cite this

Wade, A. (2007). Explicit laws of large numbers for random nearest-neighbour-type graphs.

*Advances in Applied Probability*,*39*(2), 326-342. https://doi.org/10.1239/aap/1183667613