soft_random_geometric_graph(n, radius, dim=2, pos=None, p=2, p_dist=None, seed=None)
The soft random geometric graph [1] model places n nodes uniformly at random in the unit cube in dimension :None:None:`dim`. Two nodes of distance, dist
, computed by the p-Minkowski distance metric are joined by an edge with probability :None:None:`p_dist` if the computed distance metric value of the nodes is at most radius
, 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 $O(n)$
.
This uses a k-d tree to build the graph.
The :None:None:`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 :None:None:`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)
Number of nodes or iterable of nodes
Distance threshold value
Dimension of graph
A dictionary keyed by node with node positions as values.
Which Minkowski distance metric to use. p has to meet the condition 1 <= 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 Erdős-Rényi random graph, which represents probability.
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, :None:None:`p_dist`, must be any function that takes the metric value as input and outputs a single probability value between 0-1. 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, :None:None:`p_dist`, is not supplied, the default function is an exponential distribution with rate parameter $\lambda=1$
.
Indicator of random number generation state. See Randomness<randomness>
.
A soft 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.
Returns a soft random geometric graph in the unit cube.
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.
See :Hover to see nodes names; edges to Self not shown, Caped at 50 nodes.
Using a canvas is more power efficient and can get hundred of nodes ; but does not allow hyperlinks; , arrows or text (beyond on hover)
SVG is more flexible but power hungry; and does not scale well to 50 + nodes.
All aboves nodes referred to, (or are referred from) current nodes; Edges from Self to other have been omitted (or all nodes would be connected to the central node "self" which is not useful). Nodes are colored by the library they belong to, and scaled with the number of references pointing them