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geographical_threshold_graph(n, theta, alpha=2, dim=2, pos=None, weight=None)[source]

Return a geographical threshold graph.

The geographical threshold graph model places n nodes uniformly at random in a rectangular domain. Each node \(u\) is assigned a weight \(w_u\). Two nodes \(u,v\) are connected with an edge if

\[w_u + w_v \ge \theta r^{\alpha}\]

where \(r\) is the Euclidean distance between \(u\) and \(v\), and \(\theta\), \(\alpha\) are parameters.

Parameters :

n : int

Number of nodes

theta: float

Threshold value

alpha: float, optional

Exponent of distance function

dim : int, optional

Dimension of graph

pos : dict

Node positions as a dictionary of tuples keyed by node.

weight : dict

Node weights as a dictionary of numbers keyed by node.

Returns :



If weights are not specified they are assigned to nodes by drawing randomly from an the exponential distribution with rate parameter \(\lambda=1\). To specify a weights from a different distribution assign them to a dictionary and pass it as the weight= keyword

>>> import random
>>> n = 20
>>> w=dict((i,random.expovariate(5.0)) for i in range(n))
>>> G = nx.geographical_threshold_graph(20,50,weight=w)

If node positions are not specified they are randomly assigned from the uniform distribution.


[R289]Masuda, N., Miwa, H., Konno, N.: Geographical threshold graphs with small-world and scale-free properties. Physical Review E 71, 036108 (2005)
[R290]Milan Bradonjić, Aric Hagberg and Allon G. Percus, Giant component and connectivity in geographical threshold graphs, in Algorithms and Models for the Web-Graph (WAW 2007), Antony Bonato and Fan Chung (Eds), pp. 209–216, 2007


>>> G = nx.geographical_threshold_graph(20,50)