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

Returns 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 and v are joined by 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.

  • 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.

Return type:



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


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
>>> n = 20
>>> w = {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.


[1]Masuda, N., Miwa, H., Konno, N.: Geographical threshold graphs with small-world and scale-free properties. Physical Review E 71, 036108 (2005)
[2]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