networkx.generators.geometric.thresholded_random_geometric_graph¶

thresholded_random_geometric_graph
(n, radius, theta, dim=2, pos=None, weight=None, p=2, seed=None)[source]¶ Returns a thresholded random geometric graph in the unit cube.
The thresholded random geometric graph [1] model places
n
nodes uniformly at random in the unit cube of dimensionsdim
. Each nodeu
is assigned a weight \(w_u\). Two nodesu
andv
are joined by an edge if they are within the maximum connection distance,radius
computed by thep
Minkowski distance and the summation of weights \(w_u\) + \(w_v\) is greater than or equal to the threshold parametertheta
.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
theta (float) – Threshold value
dim (int, optional) – Dimension of graph
pos (dict, optional) – A dictionary keyed by node with node positions as values.
weight (dict, optional) – Node weights as a dictionary of numbers keyed by node.
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 thresholded random geographic 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. Similarly, each node has a nodethre attribute'weight'
that stores the weight of that node as provided or as generated.Return type: Examples
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.
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
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
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)
References
[1] http://colemaclean.github.io/blog/files/thesis.pdf