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# waxman_graph¶

waxman_graph(n, alpha=0.4, beta=0.1, L=None, domain=(0, 0, 1, 1))[source]

Return a Waxman random graph.

The Waxman random graph models place n nodes uniformly at random in a rectangular domain. Two nodes u,v are connected with an edge with probability

$p = \alpha*exp(-d/(\beta*L)).$

This function implements both Waxman models.

Waxman-1: $$L$$ not specified
The distance $$d$$ is the Euclidean distance between the nodes u and v. $$L$$ is the maximum distance between all nodes in the graph.
Waxman-2: $$L$$ specified
The distance $$d$$ is chosen randomly in $$[0,L]$$.
Parameters : n : int Number of nodes alpha: float Model parameter beta: float Model parameter L : float, optional Maximum distance between nodes. If not specified the actual distance is calculated. domain : tuple of numbers, optional Domain size (xmin, ymin, xmax, ymax) G: Graph

References

 [R293] B. M. Waxman, Routing of multipoint connections. IEEE J. Select. Areas Commun. 6(9),(1988) 1617-1622.