def waxman_2_topology(n,
alpha=0.4,
beta=0.1,
domain=(0, 0, 1, 1),
distance_unit='Km',
seed=None):
r"""Return a Waxman-2 random topology.
The Waxman-2 random topology models place n nodes uniformly at random
in a rectangular domain. Two nodes u, v are connected with a link
with probability
.. math::
p = \alpha*exp(-d/(\beta*L)).
where the distance *d* is the Euclidean distance between the nodes u and v.
and *L* is the maximum distance between all nodes in the graph.
Parameters
----------
n : int
Number of nodes
alpha : float
Model parameter chosen in *(0,1]* (higher alpha increases link density)
beta : float
Model parameter chosen in *(0,1]* (higher beta increases difference
between density of short and long links)
domain : tuple of numbers, optional
Domain size (xmin, ymin, xmax, ymax)
seed : int, optional
Seed for random number generator (default=None).
Returns
-------
G : Topology
Notes
-----
Each edge of G has the attribute *length*
References
----------
.. [1] B. M. Waxman, Routing of multipoint connections.
IEEE J. Select. Areas Commun. 6(9),(1988) 1617-1622.
"""
# validate input parameters
if not isinstance(n, int) or n <= 0:
raise ValueError('n must be a positive integer')
if alpha > 1 or alpha <= 0 or beta > 1 or beta <= 0:
raise ValueError('alpha and beta must be float values in (0,1]')
if not isinstance(domain, tuple) or len(domain) != 4:
raise ValueError('domain must be a tuple of 4 number')
(xmin, ymin, xmax, ymax) = domain
if xmin > xmax:
raise ValueError('In domain, xmin cannot be greater than xmax')
if ymin > ymax:
raise ValueError('In domain, ymin cannot be greater than ymax')
if seed is not None:
random.seed(seed)
G = Topology(type='waxman_2', distance_unit=distance_unit)
G.name = "waxman_2_topology(%s, %s, %s)" % (n, alpha, beta)
G.add_nodes_from(range(n))
for v in G.nodes_iter():
G.node[v]['latitude'] = (ymin + (ymax - ymin)) * random.random()
G.node[v]['longitude'] = (xmin + (xmax - xmin)) * random.random()
l = {}
nodes = G.nodes()
while nodes:
u = nodes.pop()
for v in nodes:
x_u = G.node[u]['longitude']
x_v = G.node[v]['longitude']
y_u = G.node[u]['latitude']
y_v = G.node[v]['latitude']
l[(u, v)] = math.sqrt((x_u - x_v)**2 + (y_u - y_v)**2)
L = max(l.values())
for (u, v), d in l.items():
if random.random() < alpha * math.exp(-d / (beta * L)):
G.add_edge(u, v, length=d)
return G
def waxman_2_topology(n, alpha=0.4, beta=0.1, domain=(0, 0, 1, 1),
distance_unit='Km', seed=None):
r"""Return a Waxman-2 random topology.
The Waxman-2 random topology models place n nodes uniformly at random
in a rectangular domain. Two nodes u, v are connected with a link
with probability
.. math::
p = \alpha*exp(-d/(\beta*L)).
where the distance *d* is the Euclidean distance between the nodes u and v.
and *L* is the maximum distance between all nodes in the graph.
Parameters
----------
n : int
Number of nodes
alpha : float
Model parameter chosen in *(0,1]* (higher alpha increases link density)
beta : float
Model parameter chosen in *(0,1]* (higher beta increases difference
between density of short and long links)
domain : tuple of numbers, optional
Domain size (xmin, ymin, xmax, ymax)
seed : int, optional
Seed for random number generator (default=None).
Returns
-------
G : Topology
Notes
-----
Each edge of G has the attribute *length*
References
----------
.. [1] B. M. Waxman, Routing of multipoint connections.
IEEE J. Select. Areas Commun. 6(9),(1988) 1617-1622.
"""
# validate input parameters
if not isinstance(n, int) or n <= 0:
raise ValueError('n must be a positive integer')
if alpha > 1 or alpha <= 0 or beta > 1 or beta <= 0:
raise ValueError('alpha and beta must be float values in (0,1]')
if not isinstance(domain, tuple) or len(domain) != 4:
raise ValueError('domain must be a tuple of 4 number')
(xmin, ymin, xmax, ymax) = domain
if xmin > xmax:
raise ValueError('In domain, xmin cannot be greater than xmax')
if ymin > ymax:
raise ValueError('In domain, ymin cannot be greater than ymax')
if seed is not None:
random.seed(seed)
G = Topology(type='waxman_2', distance_unit=distance_unit)
G.name = "waxman_2_topology(%s, %s, %s)" % (n, alpha, beta)
G.add_nodes_from(range(n))
for v in G.nodes_iter():
G.node[v]['latitude'] = (ymin + (ymax - ymin)) * random.random()
G.node[v]['longitude'] = (xmin + (xmax - xmin)) * random.random()
l = {}
nodes = G.nodes()
while nodes:
u = nodes.pop()
for v in nodes:
x_u = G.node[u]['longitude']
x_v = G.node[v]['longitude']
y_u = G.node[u]['latitude']
y_v = G.node[v]['latitude']
l[(u, v)] = math.sqrt((x_u - x_v) ** 2 + (y_u - y_v) ** 2)
L = max(l.values())
for (u, v), d in l.items():
if random.random() < alpha * math.exp(-d / (beta * L)):
G.add_edge(u, v, length=d)
return G
