def find_unmatch_nodes(G):
match=[]
nodes = G.nodes()
g = nx.DiGraph()
gg = nx.DiGraph()
p0 =['+'+str(i) for i in nodes]
m0 = ['-'+str(i) for i in nodes]
for ed in G.edges():
ed1,ed2 = ed
g.add_edge('+'+str(ed1),'-'+str(ed2),capacity=1.0)
source = 'source'
sink = 'sink'
for i in p0:
#~ print p0
g.add_edge(source,i,capacity=1.0)
for i in m0:
g.add_edge(i,sink,capacity=1.0)
flow,F = nx.ford_fulkerson(g,source,sink)
for i in F:
if i not in [sink,source]:
for j in F[i]:
if j not in [sink,source]:
#~ print i,j,F[i][j]
if F[i][j] > 0:
match.append(int(j[1:]))
#~ print len(set(match))
unmatch = set(nodes)
unmatch = unmatch - set(match)
#~ print unmatch
return unmatch
def test_optional_capacity(self):
# Test optional capacity parameter.
G = nx.DiGraph()
G.add_edge('x','a', spam = 3.0)
G.add_edge('x','b', spam = 1.0)
G.add_edge('a','c', spam = 3.0)
G.add_edge('b','c', spam = 5.0)
G.add_edge('b','d', spam = 4.0)
G.add_edge('d','e', spam = 2.0)
G.add_edge('c','y', spam = 2.0)
G.add_edge('e','y', spam = 3.0)
solnFlows = {'x': {'a': 2.0, 'b': 1.0},
'a': {'c': 2.0},
'b': {'c': 0, 'd': 1.0},
'c': {'y': 2.0},
'd': {'e': 1.0},
'e': {'y': 1.0},
'y': {}}
solnValue = 3.0
s = 'x'
t = 'y'
flowValue, flowDict = nx.ford_fulkerson(G, s, t, capacity = 'spam')
assert_equal(flowValue, solnValue)
assert_equal(flowDict, solnFlows)
assert_equal(nx.min_cut(G, s, t, capacity = 'spam'), solnValue)
assert_equal(nx.max_flow(G, s, t, capacity = 'spam'), solnValue)
assert_equal(nx.ford_fulkerson_flow(G, s, t, capacity = 'spam'),
solnFlows)
def compare_flows(G, s, t, H, solnValue):
output = nx.ford_fulkerson(G, s, t)
flows = [edge[2]['flow']
for edge in output[1].edges(data = True)]
solnFlows = [H[u][v]['flow'] for (u, v) in output[1].edges()]
assert_equal((output[0], flows), (solnValue, solnFlows))
def compare_flows(G, s, t, H, solnValue):
output = nx.ford_fulkerson(G, s, t)
flows = [edge[2]['flow']
for edge in output[1].edges(data = True)]
solnFlows = [H[u][v]['flow'] for (u, v) in output[1].edges()]
assert_equal((output[0], flows), (solnValue, solnFlows))
def test_gl1(self):
G = read_graph('gl1')
s = 1
t = len(G)
validate_flows(G, s, t, 156545, *nx.ford_fulkerson(G, s, t))
validate_flows(G, s, t, 156545, nx.preflow_push_value(G, s, t),
nx.preflow_push_flow(G, s, t))
def test_gw1(self):
G = read_graph('gw1')
s = 1
t = len(G)
validate_flows(G, s, t, 1202018, *nx.ford_fulkerson(G, s, t))
validate_flows(G, s, t, 1202018, nx.preflow_push_value(G, s, t),
nx.preflow_push_flow(G, s, t))
def test_complete_graph(self):
N = 50
G = nx.complete_graph(N)
for (u, v) in G.edges():
G[u][v]['capacity'] = 5
assert_equal(nx.ford_fulkerson(G, 1, 2)[0], 5 * (N - 1))
assert_equal(nx.preflow_push(G, 1, 2)[0], 5 * (N - 1))
def test_wlm3(self):
G = read_graph('wlm3')
s = 1
t = len(G)
validate_flows(G, s, t, 11875108, *nx.ford_fulkerson(G, s, t))
validate_flows(G, s, t, 11875108, nx.preflow_push_value(G, s, t),
nx.preflow_push_flow(G, s, t))
def mincut(edges):
G = nx.DiGraph()
for i in range(n):
G.add_node(i)
for i, j, cap in edges:
if abs(cap - 1.0) <= 1e-9:
cap = 1.0
G.add_edge(i, j, capacity=cap)
source = 0
min_flow = None
edges_min_flow = None
sink_min_flow = None
for sink in range(1, n):
flow, F = nx.ford_fulkerson(G, source, sink)
if sink_min_flow is None or flow < min_flow:
sink_min_flow = sink
min_flow = flow
edges_min_flow = F.copy()
residual_edges = []
for i, j, edge_capacity in edges:
edge_flow = edges_min_flow[i][j]
if abs(edge_capacity - edge_flow) > 1e-9:
residual_edges.append((i, j))
source_component = dfs(residual_edges, source)
#print 'MinFlow:', min_flow
#print 'Component MinFlow:', source_component
return source_component, min_flow
def compare_flows(G, s, t, solnFlows, solnValue):
flowValue, flowDict = nx.ford_fulkerson(G, s, t)
assert_equal(flowValue, solnValue)
assert_equal(flowDict, solnFlows)
assert_equal(nx.min_cut(G, s, t), solnValue)
assert_equal(nx.max_flow(G, s, t), solnValue)
assert_equal(nx.ford_fulkerson_flow(G, s, t), solnFlows)
def compare_flows(G, s, t, solnFlows, solnValue):
flowValue, flowDict = nx.ford_fulkerson(G, s, t)
assert_equal(flowValue, solnValue)
assert_equal(flowDict, solnFlows)
assert_equal(nx.min_cut(G, s, t), solnValue)
assert_equal(nx.max_flow(G, s, t), solnValue)
assert_equal(nx.ford_fulkerson_flow(G, s, t), solnFlows)
def test_dimacs_digraph1(self):
#AK generator, small graph
#http://www.avglab.com/andrew/CATS/gens/ak/
[G,s,t] = nx.read_dimacs("networkx/algorithms/flow/tests/dimacs_digraph1")
value = nx.ford_fulkerson(G,s,t)[0]
compare_value_flows_vanilla_push_relabel(G,s,t,value)
compare_value_flows_relabel_to_front(G,s,t,value)
compare_value_flows_highest_label(G,s,t,value)
def get_max_flow_values(G, use_node_capacities=True, use_node_demands=False):
'''
This runs a ford-fulkerson maximum flow algrothim over the provided network
and assigns the resulting flows to each edge. The flows for each node are
also calcualted and assigned.
'''
print G.edges()
#print G.edges()
if use_node_capacities == True:
G = convert_topo(G)
print G.edges()
exit()
#check for supply and demand nodes. Needs to be at least one of each.
#if more than one need to create a super source/sink(demand) nodes.
G, supply_nodes, demand_nodes, added_nodes, added_edges = check_for_demand_supply_nodes(
G)
#get supply node and demand node
supply_nd, demand_nd = get_check_supply_demand_nodes(
G, supply_nodes, demand_nodes, added_nodes)
if use_node_capacities == True and use_node_demands == False:
#this returns the maximum flow and the flow on each edge by node
#first check a path is possible - ford-fulkerson would just return 0 otherwise
path = nx.has_path(G, supply_nd, demand_nd)
if path == False:
raise error_classes.GeneralError(
'No path exists between the supply node (node %s) and the demand node (node %s).'
% (supply_nd, demand_nd))
max_flow, edge_flows = nx.ford_fulkerson(G, supply_nd, demand_nd,
'flow_capacity')
elif use_node_capacities == True and use_node_demands == True:
#returns the flow on each edge given capacities and demands
#the sum of the demand needs to equal the sum of the supply (indicated by a negative demand value)
edge_flows = nx.min_cost_flow(G, 'demand', 'flow_capacity', 'weight')
elif use_node_capacities == False and use_node_demands == True:
#returns the flow on each edge given demands (capacities should be set at 9999999 (a very high number))
edge_flows = nx.min_cost_flow(G, 'demand', 'flow_capacity', 'weight')
#assign flows to nodes and edges
G = assign_edge_node_flows(G, edge_flows)
#before running any analysis, need to remove the added nodes and edges - the super source/demand if used
G = remove_added_nodes_edges(G, added_edges, added_nodes)
node_flow_max, edge_flow_max = get_max_flows(G)
return G, {
'max_flow': max_flow,
'max_node_flow': node_flow_max,
'max_edge_flow': edge_flow_max
}
def compare_flows(G, s, t, solnFlows, solnValue, capacity = 'capacity'):
flowValue, flowDict = nx.ford_fulkerson(G, s, t, capacity)
assert_equal(flowValue, solnValue)
assert_equal(flowDict, solnFlows)
flowValue, flowDict = nx.preflow_push(G, s, t, capacity)
assert_equal(flowValue, solnValue)
validate_flows(G, s, t, flowDict, solnValue, capacity)
assert_equal(nx.min_cut(G, s, t, capacity), solnValue)
assert_equal(nx.max_flow(G, s, t, capacity), solnValue)
assert_equal(nx.ford_fulkerson_flow(G, s, t, capacity), solnFlows)
def test_pyramid(self):
N = 10
# N = 100 # this gives a graph with 5051 nodes
G = gen_pyramid(N)
assert_almost_equal(nx.ford_fulkerson(G, (0, 0), 't')[0], 1.)
assert_almost_equal(nx.preflow_push(G, (0, 0), 't')[0], 1.)
assert_almost_equal(nx.shortest_augmenting_path(
G, (0, 0), 't', two_phase=False)[0], 1.)
assert_almost_equal(nx.shortest_augmenting_path(
G, (0, 0), 't', two_phase=True)[0], 1.)
def test_complete_graph(self):
N = 50
G = nx.complete_graph(N)
for (u, v) in G.edges():
G[u][v]['capacity'] = 5
assert_equal(nx.ford_fulkerson(G, 1, 2)[0], 5 * (N - 1))
assert_equal(nx.preflow_push(G, 1, 2)[0], 5 * (N - 1))
assert_equal(nx.shortest_augmenting_path(G, 1, 2, two_phase=False)[0],
5 * (N - 1))
assert_equal(nx.shortest_augmenting_path(G, 1, 2, two_phase=True)[0],
5 * (N - 1))
def test_digraph_infcap_path(self):
# Graph with infinite capacity (s, t)-path
G = nx.DiGraph()
G.add_edge('s', 'a')
G.add_edge('s', 'b', capacity = 30)
G.add_edge('a', 'c')
G.add_edge('b', 'c', capacity = 12)
G.add_edge('a', 't', capacity = 60)
G.add_edge('c', 't')
assert_equal(nx.ford_fulkerson(G, 's', 't'), None)
def test_gl1(self):
G = read_graph('gl1')
s = 1
t = len(G)
validate_flows(G, s, t, 156545, *nx.ford_fulkerson(G, s, t))
validate_flows(G, s, t, 156545, nx.preflow_push_value(G, s, t),
nx.preflow_push_flow(G, s, t))
validate_flows(
G, s, t, 156545,
nx.shortest_augmenting_path_value(G, s, t, two_phase=False),
nx.shortest_augmenting_path_flow(G, s, t, two_phase=False))
validate_flows(G, s, t, 156545,
nx.shortest_augmenting_path_value(G, s, t, two_phase=True),
nx.shortest_augmenting_path_flow(G, s, t, two_phase=True))
def test_wlm3(self):
G = read_graph('wlm3')
s = 1
t = len(G)
validate_flows(G, s, t, 11875108, *nx.ford_fulkerson(G, s, t))
validate_flows(G, s, t, 11875108, nx.preflow_push_value(G, s, t),
nx.preflow_push_flow(G, s, t))
validate_flows(
G, s, t, 11875108,
nx.shortest_augmenting_path_value(G, s, t, two_phase=False),
nx.shortest_augmenting_path_flow(G, s, t, two_phase=False))
validate_flows(
G, s, t, 11875108,
nx.shortest_augmenting_path_value(G, s, t, two_phase=True),
nx.shortest_augmenting_path_flow(G, s, t, two_phase=True))
def improve(G, A, score, weights):
part_num = -numpy.ones((G.shape[0], ))
aug_G = augmented_graph(G, A, score, weights=weights)
flow, F = nx.ford_fulkerson(aug_G, 's', 't')
for u, v in min_cut(aug_G, F):
if not isinstance(u, str):
part_num[u] = 1
if not isinstance(v, str):
part_num[v] = 1
P1 = numpy.where(part_num == 1)[0]
P2 = numpy.where(part_num == -1)[0]
return P1, P2
def improve(G, A, score, weights) :
part_num = -numpy.ones((G.shape[0],))
aug_G = augmented_graph(G,A,score,weights=weights)
flow,F = nx.ford_fulkerson(aug_G, 's', 't')
for u,v in min_cut(aug_G,F) :
if not isinstance(u,str) :
part_num[u] = 1
if not isinstance(v,str) :
part_num[v] = 1
P1 = numpy.where(part_num==1)[0]
P2 = numpy.where(part_num==-1)[0]
return P1,P2
def min_path_max_flow(G, s, t):
"""
Valor del flow maximal del camino minimo desde s a t.
Devuelve el flow y el path minimo:
return (flow, path)
"""
#Tiene el orden inverso al nuestro, algunos casos no van a dar bien
path = nx.shortest_path(G, s, t)
if len(path) == 2:
flow = G.get_edge_data(0, 1)["weight"]
else:
spath = nx.subgraph(G, path)
flow, _ = nx.ford_fulkerson(spath, s, t, capacity='weight')
return flow, path
def min_path_max_flow(G, s, t):
"""
Valor del flow maximal del camino minimo desde s a t.
Devuelve el flow y el path minimo:
return (flow, path)
"""
#Tiene el orden inverso al nuestro, algunos casos no van a dar bien
path = nx.shortest_path(G, s, t)
if len(path) == 2:
flow = G.get_edge_data(0, 1)["weight"]
else:
spath = nx.subgraph(G, path)
flow, _ = nx.ford_fulkerson(spath, s, t, capacity='weight')
return flow, path
def test_optional_capacity(self):
# Test optional capacity parameter.
G = nx.DiGraph()
G.add_edge('x', 'a', spam=3.0)
G.add_edge('x', 'b', spam=1.0)
G.add_edge('a', 'c', spam=3.0)
G.add_edge('b', 'c', spam=5.0)
G.add_edge('b', 'd', spam=4.0)
G.add_edge('d', 'e', spam=2.0)
G.add_edge('c', 'y', spam=2.0)
G.add_edge('e', 'y', spam=3.0)
solnFlows = {
'x': {
'a': 2.0,
'b': 1.0
},
'a': {
'c': 2.0
},
'b': {
'c': 0,
'd': 1.0
},
'c': {
'y': 2.0
},
'd': {
'e': 1.0
},
'e': {
'y': 1.0
},
'y': {}
}
solnValue = 3.0
s = 'x'
t = 'y'
flowValue, flowDict = nx.ford_fulkerson(G, s, t, capacity='spam')
assert_equal(flowValue, solnValue)
assert_equal(flowDict, solnFlows)
assert_equal(nx.min_cut(G, s, t, capacity='spam'), solnValue)
assert_equal(nx.max_flow(G, s, t, capacity='spam'), solnValue)
assert_equal(nx.ford_fulkerson_flow(G, s, t, capacity='spam'),
solnFlows)
def find_mincut_part(G,origin,terminus):
"""
Find the vertices on the origin side of a mincut of G separating origin from terminus.
"""
try: # old version of networkx
flow_rate, flow_dict=nx.ford_fulkerson(G,origin,terminus)
except AttributeError: # new version of networkx
flow_value, flow_dict = nx.maximum_flow(G, origin, terminus,flow_func=ford_fulkerson)
newverts=set([origin])
verts=set([])
while newverts:
thisvert=newverts.pop()
verts.add(thisvert)
for e in G.out_edges_iter(thisvert, data=True):
if e[2]['capacity']>flow_dict[e[0]][e[1]] and e[1] not in verts:
newverts.add(e[1])
return verts
def compare_flows(G, s, t, solnFlows, solnValue, capacity = 'capacity'):
flowValue, flowDict = nx.ford_fulkerson(G, s, t, capacity)
assert_equal(flowValue, solnValue)
assert_equal(flowDict, solnFlows)
flowValue, flowDict = nx.preflow_push(G, s, t, capacity)
assert_equal(flowValue, solnValue)
validate_flows(G, s, t, flowDict, solnValue, capacity)
flowValue, flowDict = nx.shortest_augmenting_path(G, s, t, capacity,
two_phase=False)
assert_equal(flowValue, solnValue)
validate_flows(G, s, t, flowDict, solnValue, capacity)
flowValue, flowDict = nx.shortest_augmenting_path(G, s, t, capacity,
two_phase=True)
assert_equal(flowValue, solnValue)
validate_flows(G, s, t, flowDict, solnValue, capacity)
assert_equal(nx.min_cut(G, s, t, capacity), solnValue)
assert_equal(nx.max_flow(G, s, t, capacity), solnValue)
assert_equal(nx.ford_fulkerson_flow(G, s, t, capacity), solnFlows)
def strength_of_vote_management(self, voter_profile):
# Initialize the graph weights
for pattern in self.pattern_nodes:
self.vote_management_graph["source"][pattern]['capacity'] = voter_profile[pattern]
for i in range(self.required_winners):
if pattern[i] == 1:
self.vote_management_graph[pattern][i]['capacity'] = voter_profile[pattern]
# Iterate towards the limit
r = [(float(sum(voter_profile.values())) - voter_profile[tuple([PREFERRED_MORE] * self.required_winners)]) / self.required_winners]
while len(r) < 2 or r[-2] - r[-1] > STRENGTH_TOLERANCE:
for i in range(self.required_winners):
self.vote_management_graph[i]["sink"]['capacity'] = r[-1]
max_flow = nx.ford_fulkerson(self.vote_management_graph, "source", "sink")
sink_sum = sum(v for k, v in max_flow[1].iteritems() if k[1] == "sink")
r.append(sink_sum / self.required_winners)
# We expect strengths to be above a specified threshold
if sink_sum < STRENGTH_THRESHOLD:
return 0
# Return the final max flow
return round(r[-1], 9)
def compare_flows(G, s, t, solnFlows, solnValue, capacity='capacity'):
flowValue, flowDict = nx.ford_fulkerson(G, s, t, capacity)
assert_equal(flowValue, solnValue)
assert_equal(flowDict, solnFlows)
flowValue, flowDict = nx.preflow_push(G, s, t, capacity)
assert_equal(flowValue, solnValue)
validate_flows(G, s, t, flowDict, solnValue, capacity)
flowValue, flowDict = nx.shortest_augmenting_path(G,
s,
t,
capacity,
two_phase=False)
assert_equal(flowValue, solnValue)
validate_flows(G, s, t, flowDict, solnValue, capacity)
flowValue, flowDict = nx.shortest_augmenting_path(G,
s,
t,
capacity,
two_phase=True)
assert_equal(flowValue, solnValue)
validate_flows(G, s, t, flowDict, solnValue, capacity)
assert_equal(nx.min_cut(G, s, t, capacity), solnValue)
assert_equal(nx.max_flow(G, s, t, capacity), solnValue)
assert_equal(nx.ford_fulkerson_flow(G, s, t, capacity), solnFlows)
def test_pyramid(self):
N = 10
# N = 100 # this gives a graph with 5051 nodes
G = gen_pyramid(N)
assert_almost_equal(nx.ford_fulkerson(G, (0, 0), 't')[0], 1.)
def main(argv):
file1 = argv[1]
file2 = argv[2]
file3 = argv[3]
network = nx.read_dot(file1)
#print(network)
file2 = open(file2,'r')
rawNodeCaps = file2.readlines()
nodeCaps={}
for line in rawNodeCaps:
splitLine = line.split()
nodeCaps[str(splitLine[0])]= int(splitLine[1])
airTrafficGraph = nx.DiGraph()
airTrafficGraph = nx.DiGraph(name='AirTraffic')
airTrafficGraph.add_nodes_from(network)
edgelist = []
edgetuples = network.edges()
for edgetuple in edgetuples:
tmplist =[]
tmplist.append(edgetuple[0])
tmplist.append(edgetuple[1])
edgelist.append(tmplist)
for edge in edgelist:
edge.append({"capacity":int(network[edge[0]][edge[1]][0]['label'])})
#edge.append({"label":int(network[edge[0]][edge[1]][0]['label'])})
airTrafficGraph.add_edges_from(edgelist)
## print(network.edges())
#print(airgraph.edges())
traffic = nx.read_dot(file3)
#print(traffic)
airTrafficGraph.add_nodes_from(traffic)
edgelist = []
edgetuples = traffic.edges()
for edgetuple in edgetuples:
tmplist =[]
tmplist.append(edgetuple[0])
tmplist.append(edgetuple[1])
edgelist.append(tmplist)
for edge in edgelist:
edge.append({"capacity":int(traffic[edge[0]][edge[1]][0]['label'])})
#edge.append({"label":int(network[edge[0]][edge[1]][0]['label'])})
airTrafficGraph.add_edges_from(edgelist)
airTrafficGraph=removeAntiParallelEdges(airTrafficGraph)
airTrafficGraph=removeCapConstraint(airTrafficGraph,nodeCaps)
#network=SingleSourceSink(airTrafficGraph, traffic)
plotGraph(airTrafficGraph)
'''netout = nx.write_dot(airTrafficGraph, "./airgraphout.dot")
file4 = open("./airgraphout.dot",'r')
newnet= nx.read_dot(file4)
print(newnet.to_directed())'''
flow, F =nx.ford_fulkerson(airTrafficGraph, 'S','T')
#print(flow)
for thing in F:
print thing, F[thing]
#print(network)
#unwindFlow(network,airTrafficGraph,F)
## print nodeCaps
## print (multiEdgeNodes)
## print(network.nodes())
## print("~~~~~~~~~~~~~~~~~~~")
## print(network["newnode1"]["JFK"][0]['label'])
## print(network.edges())
## print(nodeCaps)
## print(traffic)
file2.close()
#then add them to the whole list
global people
people.append(person_parameter)
return G
people = [] #empty list for people
issues = [] #empty list for issues
count1 = 0
count2 = 0
G = create_graph() #test case, as required part(e)
G = g_prime(G, people, issues)
G = g_hat(G, people, issues)
print("Total Demand on People Nodes: ", count1)
print("Total Demand on Issues Nodes: ", count2)
R = nx.ford_fulkerson(G, 'source', 'sink')
print("Max Flow: ", R[0])
print("\n")
if count1 != count2:
print("The Two Demands are not Equal")
print("Hence, may not be feasible survey")
#Fourth Problem
import networkx as nx
def createGraph(G):
#adding an edge also adds the node
G.add_edge('Spider', 'A', weight=1.0)
G.add_edge('Spider', 'H', weight=1.0)
'''
>>> import networkx as nx
>>> G = nx.DiGraph()
>>> G.add_edge('x','a', capacity=3.0)
>>> G.add_edge('x','b', capacity=1.0)
>>> G.add_edge('a','c', capacity=3.0)
>>> G.add_edge('b','c', capacity=5.0)
>>> G.add_edge('b','d', capacity=4.0)
>>> G.add_edge('d','e', capacity=2.0)
>>> G.add_edge('c','y', capacity=2.0)
>>> G.add_edge('e','y', capacity=3.0)
>>> flow, F = nx.ford_fulkerson(G, 'x', 'y')
>>> flow
3.0
'''
import networkx as nx
G = nx.DiGraph()
G.add_edge('x', 'a', capacity=3.0)
G.add_edge('x', 'b', capacity=1.0)
G.add_edge('a', 'c', capacity=3.0)
G.add_edge('b', 'c', capacity=5.0)
G.add_edge('b', 'd', capacity=4.0)
G.add_edge('d', 'e', capacity=2.0)
G.add_edge('c', 'y', capacity=2.0)
G.add_edge('e', 'y', capacity=3.0)
flow, F = nx.ford_fulkerson(G, 'x', 'y')
print(flow)
print(F)
def test_pyramid(self):
N = 10
# N = 100 # this gives a graph with 5051 nodes
G = gen_pyramid(N)
assert_almost_equal(nx.ford_fulkerson(G, (0, 0), 't')[0], 1.)
def minimum_st_edge_cut(G, s, t, capacity='capacity'):
"""Returns the edges of the cut-set of a minimum (s, t)-cut.
We use the max-flow min-cut theorem, i.e., the capacity of a minimum
capacity cut is equal to the flow value of a maximum flow.
Parameters
----------
G : NetworkX graph
Edges of the graph are expected to have an attribute called
'capacity'. If this attribute is not present, the edge is
considered to have infinite capacity.
s : node
Source node for the flow.
t : node
Sink node for the flow.
capacity: string
Edges of the graph G are expected to have an attribute capacity
that indicates how much flow the edge can support. If this
attribute is not present, the edge is considered to have
infinite capacity. Default value: 'capacity'.
Returns
-------
cutset : set
Set of edges that, if removed from the graph, will disconnect it
Raises
------
NetworkXUnbounded
If the graph has a path of infinite capacity, all cuts have
infinite capacity and the function raises a NetworkXError.
Examples
--------
>>> G = nx.DiGraph()
>>> G.add_edge('x','a', capacity = 3.0)
>>> G.add_edge('x','b', capacity = 1.0)
>>> G.add_edge('a','c', capacity = 3.0)
>>> G.add_edge('b','c', capacity = 5.0)
>>> G.add_edge('b','d', capacity = 4.0)
>>> G.add_edge('d','e', capacity = 2.0)
>>> G.add_edge('c','y', capacity = 2.0)
>>> G.add_edge('e','y', capacity = 3.0)
>>> sorted(nx.minimum_edge_cut(G, 'x', 'y'))
[('c', 'y'), ('x', 'b')]
>>> nx.minimum_cut_value(G, 'x', 'y')
3.0
"""
try:
H = nx.ford_fulkerson(G, s, t, capacity=capacity)
cutset = set()
# Compute reachable nodes from source in the residual network
reachable = set(nx.single_source_shortest_path(H,s))
# And unreachable nodes
others = set(H) - reachable # - set([s])
# Any edge in the original network linking these two partitions
# is part of the edge cutset
for u, nbrs in ((n, G[n]) for n in reachable):
cutset.update((u,v) for v in nbrs if v in others)
return cutset
except nx.NetworkXUnbounded:
# Should we raise any other exception or just let ford_fulkerson
# propagate nx.NetworkXUnbounded ?
raise nx.NetworkXUnbounded("Infinite capacity path, no minimum cut.")
def test_complete_graph(self):
N = 50
G = nx.complete_graph(N)
for (u, v) in G.edges():
G[u][v]['capacity'] = 5
assert_equal(nx.ford_fulkerson(G, 1, 2)[0], 5 * (N - 1))