# Explicit laws of large numbers for random nearest-neighbour-type graphs

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23 Citations (Scopus)

## 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 $R^d$, $d \in N$. 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.
Translated title of the contribution Explicit laws of large numbers for random nearest-neighbour-type graphs English 326 - 342 17 Advances in Applied Probability 39 (2) https://doi.org/10.1239/aap/1183667613 Published - Jun 2007

### Bibliographical note

Publisher: Applied Probability Trust