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 model places n nodes uniformly at random in a rectangular domain. Each pair of nodes at Euclidean distance $d$ is joined by an edge with probability

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

This function implements both Waxman models, using the L keyword argument.

Waxman-1: if L is not specified, it is set to be the maximum distance between any pair of nodes.
Waxman-2: if L is specified, the distance between a pair of nodes is chosen uniformly at random from the interval $[0, L]$ .

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 (four-tuple of numbers, optional) – Domain size, given as a tuple of the form $(x_min, y_min, x_max, y_max)$ .
Returns:	G
Return type:	Graph

References

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