On the Connectivity of Random k-th Nearest Neighbour Graphs

Model 1. Consider the complete graph K n , with vertex set [n] = {1, 2,…, n }, in which each edge e is assigned a length X e . Colour the k shortest edges incident with each vertex green and the remaining edges blue. The graph made up of the green edges only, will be referred to as the k-th nearest neighbour graph . This graph has been studied in a variety of contexts both computational and statistical.

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