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