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)

Returns:

G: Graph

References

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