networkx.random_geometric_graph¶

networkx.random_geometric_graph(n, radius, dim=2, pos=None, metric=None)[source]¶

Returns a random geometric graph in the unit cube.

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.

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. metric : function A metric on vectors of numbers (represented as lists or tuples). This must be a function that accepts two lists (or tuples) as input and yields a number as output. The function must also satisfy the four requirements of a metric. Specifically, if d is the function and x, y, and z are vectors in the graph, then d must satisfy d*(*x, y) ≥ 0, d*(*x, y) = 0 if and only if x = y, d*(*x, y) = d*(*y, x), d*(*x, z) ≤ d*(*x, y) + d*(*y, z). If this argument is not specified, the Euclidean distance metric is used.

Returns:

Graph 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.

Notes

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

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
>>> p = {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

[R1229]

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

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)

Specify an alternate distance metric using the metric keyword argument. For example, to use the “taxicab metric” instead of the default Euclidean metric:

>>> dist = lambda x, y: sum(abs(a - b) for a, b in zip(x, y))
>>> G = nx.random_geometric_graph(10, 0.1, metric=dist)