def _is_k_connected(args:argparse.ArgumentParser):
"""
Description: Check if network is k-connected
Args:
args (obj): An object with all user arguments
Returns:
boolean
"""
global new_G
if args == None:
return nx.is_k_edge_connected(new_G, k=3)
return nx.is_k_edge_connected(new_G, k=int(args.k))
def getPossibleEONsWithNewLinks(eon, max_length=None, n_links=1, k_edge_connected=None, possible_links=None):
if possible_links is None:
possible_links = getPossibleNewLinks(eon, max_length, n_links)
for links in possible_links:
H = deepcopy(eon)
for link in links:
H.addLink(link[0], link[1], link[2])
if k_edge_connected is None or nx.is_k_edge_connected(H, k_edge_connected):
H.name = 'EON with %d links'%len(H.edges())
H.resetSpectrum()
H.initializeRoutes()
yield H
def k_edge_augmentation(G, k, avail=None, weight=None, partial=False):
"""Finds set of edges to k-edge-connect G.
Adding edges from the augmentation to G make it impossible to disconnect G
unless k or more edges are removed. This function uses the most efficient
function available (depending on the value of k and if the problem is
weighted or unweighted) to search for a minimum weight subset of available
edges that k-edge-connects G. In general, finding a k-edge-augmentation is
NP-hard, so solutions are not garuenteed to be minimal. Furthermore, a
k-edge-augmentation may not exist.
Parameters
----------
G : NetworkX graph
An undirected graph.
k : integer
Desired edge connectivity
avail : dict or a set of 2 or 3 tuples
The available edges that can be used in the augmentation.
If unspecified, then all edges in the complement of G are available.
Otherwise, each item is an available edge (with an optinal weight).
In the unweighted case, each item is an edge ``(u, v)``.
In the weighted case, each item is a 3-tuple ``(u, v, d)`` or a dict
with items ``(u, v): d``. The third item, ``d``, can be a dictionary
or a real number. If ``d`` is a dictionary ``d[weight]``
correspondings to the weight.
weight : string
key to use to find weights if ``avail`` is a set of 3-tuples where the
third item in each tuple is a dictionary.
partial : boolean
If partial is True and no feasible k-edge-augmentation exists, then all
a partial k-edge-augmentation is generated. Adding the edges in a
partial augmentation to G, minimizes the number of k-edge-connected
components and maximizes the edge connectivity between those
components. For details, see :func:`partial_k_edge_augmentation`.
Yields
------
edge : tuple
Edges that, once added to G, would cause G to become k-edge-connected.
If partial is False, an error is raised if this is not possible.
Otherwise, generated edges form a partial augmentation, which
k-edge-connects any part of G where it is possible, and maximally
connects the remaining parts.
Raises
------
NetworkXUnfeasible:
If partial is False and no k-edge-augmentation exists.
NetworkXNotImplemented:
If the input graph is directed or a multigraph.
ValueError:
If k is less than 1
Notes
-----
When k=1 this returns an optimal solution.
When k=2 and ``avail`` is None, this returns an optimal solution.
Otherwise when k=2, this returns a 2-approximation of the optimal solution.
For k>3, this problem is NP-hard and this uses a randomized algorithm that
produces a feasible solution, but provides no gaurentees on the
solution weight.
Example
-------
>>> # Unweighted cases
>>> G = nx.path_graph((1, 2, 3, 4))
>>> G.add_node(5)
>>> sorted(nx.k_edge_augmentation(G, k=1))
[(1, 5)]
>>> sorted(nx.k_edge_augmentation(G, k=2))
[(1, 5), (5, 4)]
>>> sorted(nx.k_edge_augmentation(G, k=3))
[(1, 4), (1, 5), (2, 5), (3, 5), (4, 5)]
>>> complement = list(nx.k_edge_augmentation(G, k=5, partial=True))
>>> G.add_edges_from(complement)
>>> nx.edge_connectivity(G)
4
Example
-------
>>> # Weighted cases
>>> G = nx.path_graph((1, 2, 3, 4))
>>> G.add_node(5)
>>> # avail can be a tuple with a dict
>>> avail = [(1, 5, {'weight': 11}), (2, 5, {'weight': 10})]
>>> sorted(nx.k_edge_augmentation(G, k=1, avail=avail, weight='weight'))
[(2, 5)]
>>> # or avail can be a 3-tuple with a real number
>>> avail = [(1, 5, 11), (2, 5, 10), (4, 3, 1), (4, 5, 51)]
>>> sorted(nx.k_edge_augmentation(G, k=2, avail=avail))
[(1, 5), (2, 5), (4, 5)]
>>> # or avail can be a dict
>>> avail = {(1, 5): 11, (2, 5): 10, (4, 3): 1, (4, 5): 51}
>>> sorted(nx.k_edge_augmentation(G, k=2, avail=avail))
[(1, 5), (2, 5), (4, 5)]
>>> # If augmentation is infeasible, then a partial solution can be found
>>> avail = {(1, 5): 11}
>>> sorted(nx.k_edge_augmentation(G, k=2, avail=avail, partial=True))
[(1, 5)]
"""
try:
if k <= 0:
raise ValueError('k must be a positive integer, not {}'.format(k))
elif G.number_of_nodes() < k + 1:
msg = 'impossible to {} connect in graph with less than {} nodes'
raise nx.NetworkXUnfeasible(msg.format(k, k + 1))
elif avail is not None and len(avail) == 0:
if not nx.is_k_edge_connected(G, k):
raise nx.NetworkXUnfeasible('no available edges')
aug_edges = []
elif k == 1:
aug_edges = one_edge_augmentation(G,
avail=avail,
weight=weight,
partial=partial)
elif k == 2:
aug_edges = bridge_augmentation(G, avail=avail, weight=weight)
else:
# raise NotImplementedError(
# 'not implemented for k>2. k={}'.format(k))
aug_edges = greedy_k_edge_augmentation(G,
k=k,
avail=avail,
weight=weight,
seed=0)
# Do eager evaulation so we can catch any exceptions
# Before executing partial code.
for edge in list(aug_edges):
yield edge
except nx.NetworkXUnfeasible:
if partial:
# Return all available edges
if avail is None:
aug_edges = complement_edges(G)
else:
# If we cant k-edge-connect the entire graph, try to
# k-edge-connect as much as possible
aug_edges = partial_k_edge_augmentation(G,
k=k,
avail=avail,
weight=weight)
for edge in aug_edges:
yield edge
else:
raise
def k_edge_augmentation(G, k, avail=None, weight=None, partial=False):
"""Finds set of edges to k-edge-connect G.
Adding edges from the augmentation to G make it impossible to disconnect G
unless k or more edges are removed. This function uses the most efficient
function available (depending on the value of k and if the problem is
weighted or unweighted) to search for a minimum weight subset of available
edges that k-edge-connects G. In general, finding a k-edge-augmentation is
NP-hard, so solutions are not garuenteed to be minimal. Furthermore, a
k-edge-augmentation may not exist.
Parameters
----------
G : NetworkX graph
An undirected graph.
k : integer
Desired edge connectivity
avail : dict or a set of 2 or 3 tuples
The available edges that can be used in the augmentation.
If unspecified, then all edges in the complement of G are available.
Otherwise, each item is an available edge (with an optinal weight).
In the unweighted case, each item is an edge ``(u, v)``.
In the weighted case, each item is a 3-tuple ``(u, v, d)`` or a dict
with items ``(u, v): d``. The third item, ``d``, can be a dictionary
or a real number. If ``d`` is a dictionary ``d[weight]``
correspondings to the weight.
weight : string
key to use to find weights if ``avail`` is a set of 3-tuples where the
third item in each tuple is a dictionary.
partial : boolean
If partial is True and no feasible k-edge-augmentation exists, then all
a partial k-edge-augmentation is generated. Adding the edges in a
partial augmentation to G, minimizes the number of k-edge-connected
components and maximizes the edge connectivity between those
components. For details, see :func:`partial_k_edge_augmentation`.
Yields
------
edge : tuple
Edges that, once added to G, would cause G to become k-edge-connected.
If partial is False, an error is raised if this is not possible.
Otherwise, generated edges form a partial augmentation, which
k-edge-connects any part of G where it is possible, and maximally
connects the remaining parts.
Raises
------
NetworkXUnfeasible:
If partial is False and no k-edge-augmentation exists.
NetworkXNotImplemented:
If the input graph is directed or a multigraph.
ValueError:
If k is less than 1
Notes
-----
When k=1 this returns an optimal solution.
When k=2 and ``avail`` is None, this returns an optimal solution.
Otherwise when k=2, this returns a 2-approximation of the optimal solution.
For k>3, this problem is NP-hard and this uses a randomized algorithm that
produces a feasible solution, but provides no gaurentees on the
solution weight.
Example
-------
>>> # Unweighted cases
>>> G = nx.path_graph((1, 2, 3, 4))
>>> G.add_node(5)
>>> sorted(nx.k_edge_augmentation(G, k=1))
[(1, 5)]
>>> sorted(nx.k_edge_augmentation(G, k=2))
[(1, 5), (5, 4)]
>>> sorted(nx.k_edge_augmentation(G, k=3))
[(1, 4), (1, 5), (2, 5), (3, 5), (4, 5)]
>>> complement = list(nx.k_edge_augmentation(G, k=5, partial=True))
>>> G.add_edges_from(complement)
>>> nx.edge_connectivity(G)
4
Example
-------
>>> # Weighted cases
>>> G = nx.path_graph((1, 2, 3, 4))
>>> G.add_node(5)
>>> # avail can be a tuple with a dict
>>> avail = [(1, 5, {'weight': 11}), (2, 5, {'weight': 10})]
>>> sorted(nx.k_edge_augmentation(G, k=1, avail=avail, weight='weight'))
[(2, 5)]
>>> # or avail can be a 3-tuple with a real number
>>> avail = [(1, 5, 11), (2, 5, 10), (4, 3, 1), (4, 5, 51)]
>>> sorted(nx.k_edge_augmentation(G, k=2, avail=avail))
[(1, 5), (2, 5), (4, 5)]
>>> # or avail can be a dict
>>> avail = {(1, 5): 11, (2, 5): 10, (4, 3): 1, (4, 5): 51}
>>> sorted(nx.k_edge_augmentation(G, k=2, avail=avail))
[(1, 5), (2, 5), (4, 5)]
>>> # If augmentation is infeasible, then a partial solution can be found
>>> avail = {(1, 5): 11}
>>> sorted(nx.k_edge_augmentation(G, k=2, avail=avail, partial=True))
[(1, 5)]
"""
try:
if k <= 0:
raise ValueError('k must be a positive integer, not {}'.format(k))
elif G.number_of_nodes() < k + 1:
msg = 'impossible to {} connect in graph with less than {} nodes'
raise nx.NetworkXUnfeasible(msg.format(k, k + 1))
elif avail is not None and len(avail) == 0:
if not nx.is_k_edge_connected(G, k):
raise nx.NetworkXUnfeasible('no available edges')
aug_edges = []
elif k == 1:
aug_edges = one_edge_augmentation(G, avail=avail, weight=weight,
partial=partial)
elif k == 2:
aug_edges = bridge_augmentation(G, avail=avail, weight=weight)
else:
# raise NotImplementedError(
# 'not implemented for k>2. k={}'.format(k))
aug_edges = greedy_k_edge_augmentation(
G, k=k, avail=avail, weight=weight, seed=0)
# Do eager evaulation so we can catch any exceptions
# Before executing partial code.
for edge in list(aug_edges):
yield edge
except nx.NetworkXUnfeasible:
if partial:
# Return all available edges
if avail is None:
aug_edges = complement_edges(G)
else:
# If we cant k-edge-connect the entire graph, try to
# k-edge-connect as much as possible
aug_edges = partial_k_edge_augmentation(G, k=k, avail=avail,
weight=weight)
for edge in aug_edges:
yield edge
else:
raise
def is_k_edge_connected(G, k):
return nx.is_k_edge_connected(G, k)
def score(gg):
if not nx.is_k_edge_connected(gg, 2):
return None
#return sum(sorted(nx.get_edge_attributes(g, "points").values())[-4:])
return sum(nx.get_edge_attributes(g, "points").values())
