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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 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.