random_geometric_graph¶

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:	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)

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)

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

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