# networkx.generators.geometric.random_geometric_graph¶

random_geometric_graph(n, radius, dim=2, pos=None, p=2, seed=None)[source]

Returns a random geometric graph in the unit cube of dimensions dim.

The random geometric graph model places n nodes uniformly at random in the unit cube. Two nodes are joined by an edge if the distance between the nodes is at most radius.

Edges are determined using a KDTree when SciPy is available. This reduces the time complexity from $$O(n^2)$$ to $$O(n)$$.

Parameters
• n (int or iterable) – Number of nodes or iterable 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.

• p (float, optional) – Which Minkowski distance metric to use. p has to meet the condition 1 <= p <= infinity.

If this argument is not specified, the $$L^2$$ metric (the Euclidean distance metric), p = 2 is used. This should not be confused with the p of an Erdős-Rényi random graph, which represents probability.

• seed (integer, random_state, or None (default)) – Indicator of random number generation state. See Randomness.

Returns

A random geometric graph, undirected and without self-loops. Each node has a node attribute 'pos' that stores the position of that node in Euclidean space as provided by the pos keyword argument or, if pos was not provided, as generated by this function.

Return type

Graph

Examples

Create a random geometric graph on twenty nodes where nodes are joined by an edge if their distance is at most 0.1:

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


Notes

This uses a k-d tree to build the graph.

The pos keyword argument can be used to specify node positions so you can create an arbitrary distribution and domain for positions.

For example, to use a 2D Gaussian distribution of node positions with mean (0, 0) and standard deviation 2:

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


References

1

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