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

Andrew Wade

Research output: Contribution to journalArticlepeer-review

24 Citations (Scopus)


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 languageEnglish
Pages (from-to)326-342
Number of pages17
JournalAdvances in Applied Probability
Issue number2
Publication statusPublished - Jun 2007


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


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