# On the One dimensional Poisson Random Geometric Graph - Mathematics > Probability

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Abstract: Given a Poisson process on a bounded interval, its random geometric graph isthe graph whose vertices are the points of the Poisson process and edges existbetween two points if and only if their distance is less than a fixed giventhreshold. We compute explicitly the distribution of the number of connectedcomponents of this graph. The proof relies on inverting some Laplacetransforms.

Author: ** Laurent Decreusefond LTCI, Eduardo Ferraz LTCI**

Source: https://arxiv.org/