The Distribution of the Number of Isolated Nodes in the 1-Dimensional Soft Random Geometric Graph
We study the number of isolated nodes in a soft random geometric graph whose vertices constitute a Poisson process on the torus of length L (the line segment [0 ,L ] with periodic boundary conditions), and where an edge is present between two nodes with a probability which depends on the distance between them. Edges between distinct pairs of nodes are mutually independent. In a suitable scaling regime, we show that the number of isolated nodes converges in total variation to a Poisson random variable. The result implies an upper bound on the probability that the random graph is connected
Year of publication: |
[2022]
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Authors: | Wilsher, Michael ; Dettmann, Carl ; Ganesh, A.J |
Publisher: |
[S.l.] : SSRN |
Subject: | Graphentheorie | Graph theory |
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