Geodesic
A strong law of large numbers for random biased connected graphs
Teoretičeskaâ i matematičeskaâ fizika, Tome 172 (2012) no. 3, pp. 344-354 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider a class of random connected graphs with random vertices and random edges in which the randomness of the vertices is determined by a continuous probability distribution and the randomness of the edges is determined by a connection function. We derive a strong law of large numbers on the total lengths of all random edges for a random biased connected graph that is a generalization of a directed $k$-nearest-neighbor graph.
Keywords: random connected graph, random biased connected graph, law of large numbers. 
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Zhonghao Xu; Ya. Higuchi; Chunhua. A strong law of large numbers for random biased connected graphs. Teoretičeskaâ i matematičeskaâ fizika, Tome 172 (2012) no. 3, pp. 344-354. http://geodesic.mathdoc.fr/item/TMF_2012_172_3_a1/

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