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# random_geometric_graph¶

Return the random geometric graph in the unit cube.

The random geometric graph model places n nodes uniformly at random in the unit cube Two nodes $$u,v$$ are connected with an edge if $$d(u,v)<=r$$ where $$d$$ is the Euclidean distance and $$r$$ is a radius threshold.

Parameters : n : int Number of nodes radius: float Distance threshold value dim : int, optional Dimension of graph pos : dict, optional A dictionary keyed by node with node positions as values. Graph

Notes

This uses an $$n^2$$ algorithm to build the graph. A faster algorithm is possible using k-d trees.

The pos keyword can be used to specify node positions so you can create an arbitrary distribution and domain for positions. If you need a distance function other than Euclidean you’ll have to hack the algorithm.

E.g to use a 2d Gaussian distribution of node positions with mean (0,0) and std. dev. 2

>>> import random
>>> n=20
>>> p=dict((i,(random.gauss(0,2),random.gauss(0,2))) for i in range(n))
>>> G = nx.random_geometric_graph(n,0.2,pos=p)


References

 [R292] Penrose, Mathew, Random Geometric Graphs, Oxford Studies in Probability, 5, 2003.

Examples

>>> G = nx.random_geometric_graph(20,0.1)