networkx.generators.geometric.soft_random_geometric_graph¶

soft_random_geometric_graph
(n, radius, dim=2, pos=None, p=2, p_dist=None, seed=None)[source]¶ Returns a soft random geometric graph in the unit cube.
The soft random geometric graph [1] model places
n
nodes uniformly at random in the unit cube in dimensiondim
. Two nodes of distance,dist
, computed by thep
Minkowski distance metric are joined by an edge with probabilityp_dist
if the computed distance metric value of the nodes is at mostradius
, otherwise they are not joined.Edges within
radius
of each other 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.p_dist (function, optional) – A probability density function computing the probability of connecting two nodes that are of distance, dist, computed by the Minkowski distance metric. The probability density function,
p_dist
, must be any function that takes the metric value as input and outputs a single probability value between 01. The scipy.stats package has many probability distribution functions implemented and tools for custom probability distribution definitions [2], and passing the .pdf method of scipy.stats distributions can be used here. If the probability function,p_dist
, is not supplied, the default function is an exponential distribution with rate parameter \(\lambda=1\).seed (integer, random_state, or None (default)) – Indicator of random number generation state. See Randomness.
 Returns
A soft 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
Default Graph:
G = nx.soft_random_geometric_graph(50, 0.2)
Custom Graph:
Create a soft random geometric graph on 100 uniformly distributed nodes where nodes are joined by an edge with probability computed from an exponential distribution with rate parameter \(\lambda=1\) if their Euclidean distance is at most 0.2.
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
The scipy.stats package can be used to define the probability distribution with the .pdf method used as
p_dist
.>>> import random >>> import math >>> n = 100 >>> pos = {i: (random.gauss(0, 2), random.gauss(0, 2)) for i in range(n)} >>> p_dist = lambda dist : math.exp(dist) >>> G = nx.soft_random_geometric_graph(n, 0.2, pos=pos, p_dist=p_dist)
References
 1
 Penrose, Mathew D. “Connectivity of soft random geometric graphs.”
The Annals of Applied Probability 26.2 (2016): 9861028.
 [2] scipy.stats 
https://docs.scipy.org/doc/scipy/reference/tutorial/stats.html