Random geometric graph
Encyclopedia
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
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.
Graph theory
In mathematics and computer science, graph theory is the study of graphs, mathematical structures used to model pairwise relations between objects from a certain collection. A "graph" in this context refers to a collection of vertices or 'nodes' and a collection of edges that connect pairs of...
, a random geometric graph is a random undirected graph drawn on a bounded region, eg. the unit torus
It is generated by
- Placing vertices at random uniformly and independentlyStatistical independenceIn probability theory, to say that two events are independent intuitively means that the occurrence of one event makes it neither more nor less probable that the other occurs...
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.