geographical_threshold_graph¶
- 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
is assigned a weight
. Two nodes
and
are joined by an edge if
where
is the Euclidean distance between
and
, and
,
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: Return type: Graph
Examples
>>> G = nx.geographical_threshold_graph(20, 50)
Notes
If weights are not specified they are assigned to nodes by drawing randomly from the exponential distribution with rate parameter
. 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.
References
[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