Random geometric graph


Random geometric graph

In graph theory, a random geometric graph is a random undirected graph drawn on a bounded region, eg. the unit torus [0, 1)2.It is generated by
# Placing vertices at random uniformly and independently on the region
# Connecting two vertices, "u", "v" if and only if the distance between them is at most a threshold "r", ie. "d" ("u", "v") ≤ "r".

Several probabilistic results are known about the number of components in the graph as a function of the threshold "r" and the number of vertices "n".

References

* Penrose, Mathew: "Random Geometric Graphs" (Oxford Studies in Probability, 5), 2003.


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