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A strong law of large numbers for random biased connected graphs |
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| Authors: | Zhonghao Xu Y Higuchi Chunhua Hu |
| Institution: | 1. School of Finance and Statistics, East China Normal University, Shanghai, China 2. Department of Mathematics, Kobe University, Kobe, Japan 3. School of Applied Mathematics, Beijing Normal University, Zhuhai, China |
| 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. |
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