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 mostradius
.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 condition1 <= 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 ErdősRényi 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 selfloops. Each node has a node attribute
'pos'
that stores the position of that node in Euclidean space as provided by thepos
keyword argument or, ifpos
was not provided, as generated by this function.Return type: 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 kd 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.