- Random geometric graph
In

graph theory , a**random geometric graph**is a randomundirected 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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