waxman_graph¶

waxman_graph(n, alpha=0.40000000000000002, beta=0.10000000000000001, 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)

Returns :

G: Graph :

References

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