thresholded_random_geometric_graph(n, radius, theta, dim=2, pos=None, weight=None, p=2, seed=None)
The thresholded random geometric graph [1] model places n nodes uniformly at random in the unit cube of dimensions :None:None:`dim`. Each node u is assigned a weight $w_u$
. Two nodes u and :None:None:`v` are joined by an edge if they are within the maximum connection distance, radius
computed by the p-Minkowski distance and the summation of weights $w_u$
+ $w_v$
is greater than or equal to the threshold parameter :None:None:`theta`.
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
If weights are not specified they are assigned to nodes by drawing randomly from the exponential distribution with rate parameter $\lambda=1$
. To specify weights from a different distribution, use the :None:None:`weight` keyword argument:
::
>>> import random
>>> import math
>>> n = 50
>>> pos = {i: (random.gauss(0, 2), random.gauss(0, 2)) for i in range(n)}
>>> w = {i: random.expovariate(5.0) for i in range(n)}
>>> G = nx.thresholded_random_geometric_graph(n, 0.2, 0.1, 2, pos, w)
Number of nodes or iterable of nodes
Distance threshold value
Threshold value
Dimension of graph
A dictionary keyed by node with node positions as values.
Node weights as a dictionary of numbers keyed by node.
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.
Indicator of random number generation state. See Randomness<randomness>
.
A thresholded random geographic 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. Similarly, each node has a nodethre attribute 'weight'
that stores the weight of that node as provided or as generated.
Returns a thresholded random geometric graph in the unit cube.
Default Graph:
G = nx.thresholded_random_geometric_graph(50, 0.2, 0.1)
Custom Graph:
Create a thresholded random geometric graph on 50 uniformly distributed nodes where nodes are joined by an edge if their sum weights drawn from a exponential distribution with rate = 5 are >= theta = 0.1 and 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