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Teoreticheskaya i Matematicheskaya Fizika, 2012, Volume 172, Number 3, Pages 344–354
DOI: https://doi.org/10.4213/tmf6962 (Mi tmf6962) 		 
A strong law of large numbers for random biased connected graphs

Zhonghao Xua, Ya. Higuchib, Chunhuac

a School of Finance and Statistics, East China Normal University, Shanghai, China
b Department of Mathematics, Kobe University, Kobe, Japan
c School of Applied Mathematics, Beijing Normal University, Zhuhai, China
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DOI: https://doi.org/10.4213/tmf6962
Abstract: 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.
Received: 17.01.2012
English version:
Theoretical and Mathematical Physics, 2012, Volume 172, Issue 3, Pages 1177–1186
DOI: https://doi.org/10.1007/s11232-012-0106-6
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: Zhonghao Xu, Ya. Higuchi, Chunhua, “A strong law of large numbers for random biased connected graphs”, TMF, 172:3 (2012), 344–354; Theoret. and Math. Phys., 172:3 (2012), 1177–1186
Citation in format AMSBIB
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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