def getVmax(G, S, L):
V = G.nodes()
# flow[i][j] = max-flow in (S, V) when S[i] is swapped with V[j]
flow = [[None for _ in xrange(len(V))] for _ in xrange(len(S))]
setS = set(S)
without_swap_flow = nx.maximum_flow_value(getFlowGraph(G, S, L), 's', 't')
for i in xrange(len(S)):
for j in xrange(len(V)):
if V[j] not in setS:
temp = S[i]
S[i] = V[j]
flow_graph = getFlowGraph(G, S, L)
flow[i][j] = nx.maximum_flow_value(flow_graph, 's',
't') > without_swap_flow
S[i] = temp
swap_pair = []
for i in xrange(len(S)):
for j in xrange(len(V)):
swap_pair.append([i, j])
if swap_pair:
i, j = choice(swap_pair)
else:
return S
S[i] = V[j]
return S
def compute_capacity(self, node):
if node == self.identity:
return
contribution = nx.maximum_flow_value(self.graph, node, self.identity)
consumption = nx.maximum_flow_value(self.graph, self.identity, node)
self.graph.add_node(node, capacity=max(0, contribution - consumption))
self.graph.add_node(node, bartercast=contribution - consumption)
def doOneSwaps(G, S, L):
Vmax = getVmax(G, S[:], L)
while nx.maximum_flow_value(getFlowGraph(G, Vmax, L), 's',
't') > nx.maximum_flow_value(
getFlowGraph(G, S, L), 's', 't'):
S = Vmax
Vmax = getVmax(G, S[:], L)
return S
def tst():
G = nx.DiGraph()
edges = [(0, 1, {
'capacity': 5,
'weight': 1
}), (0, 2, {
'capacity': 3,
'weight': 0.5
}), (0, 3, {
'capacity': 1,
'weight': 1
}), (4, 6, {
'capacity': 4,
'weight': 1
}), (5, 6, {
'capacity': 5,
'weight': 1
}), (1, 4, {
'capacity': np.inf,
'weight': 1
}), (2, 4, {
'capacity': np.inf,
'weight': 1
}), (3, 5, {
'capacity': np.inf,
'weight': 1
})]
G.add_edges_from(edges)
mincostflow = nx.max_flow_min_cost(G, 0, 6)
mincost = nx.cost_of_flow(G, mincostflow)
max_flow = nx.maximum_flow_value(G, 0, 6)
def algorithm_maximum_flow(graph):
graph.add_edge('s', '1', capacity=8)
graph.add_edge('1', 's', capacity=2)
graph.add_edge('s', '2', capacity=11)
graph.add_edge('2', 's', capacity=159)
graph.add_edge('s', '3', capacity=159)
graph.add_edge('3', 's', capacity=20)
graph.add_edge('s', '4', capacity=12)
graph.add_edge('4', 's', capacity=11)
graph.add_edge('1', '2', capacity=2)
graph.add_edge('2', '1', capacity=2)
graph.add_edge('1', '3', capacity=1)
graph.add_edge('3', '1', capacity=15)
graph.add_edge('1', '4', capacity=2)
graph.add_edge('4', '1', capacity=1)
graph.add_edge('2', '3', capacity=7)
graph.add_edge('3', '2', capacity=8)
graph.add_edge('2', 't', capacity=8)
graph.add_edge('t', '2', capacity=11)
graph.add_edge('3', '4', capacity=0)
graph.add_edge('4', '3', capacity=15)
graph.add_edge('3', 't', capacity=99)
graph.add_edge('t', '3', capacity=12)
graph.add_edge('4', 't', capacity=12)
graph.add_edge('t', '4', capacity=2)
result = nx.maximum_flow_value(graph, 's', 't')
print("Max flow: " + str(result))
def Time(G, name):
dic = {
"Fuente": [],
"Sumidero": [],
"Media": [],
"Mediana": [],
"Std": [],
"MaxFlow": []
}
Nodes = G.nodes
for i in Nodes:
for j in Nodes:
if i != j:
t = []
for k in range(10):
t.append(Edmond(G, i, j))
dic["Fuente"].append(i)
dic["Sumidero"].append(j)
dic["Media"].append(np.mean(t))
dic["Mediana"].append(np.median(t))
dic["Std"].append(np.std(t))
dic["MaxFlow"].append(
nx.maximum_flow_value(G, i, j, capacity="weight"))
df = pd.DataFrame(dic)
df.to_csv(name, index=None)
def _chk_cap_flow(anal_graph: DiGraph, capability_info: ComponentInfo,
in_ports: Iterable[ICaseString], out_ports: Iterable[object],
port_name_func: Callable[[ICaseString], object]) -> None:
"""Check the flow capacity for the given capability and ports.
`anal_graph` is the analysis graph.
`capability_info` is the capability information.
`in_ports` are the input ports supporting the given capability.
`out_ports` are the output ports of the original processor.
`port_name_func` is the port reporting name function.
The function raises a BlockedCapError if the capability through any
input port can't flow with full or partial capacity from this input
port to the output ports.
"""
unit_anal_map = {
unit_attrs[_OLD_NODE_KEY]: unit
for unit, unit_attrs in anal_graph.nodes(True)
}
unified_out = _aug_out_ports(anal_graph,
[unit_anal_map[port] for port in out_ports])
unified_out = _split_nodes(anal_graph)[unified_out]
_dist_edge_caps(anal_graph)
for cur_port in in_ports:
_chk_unit_flow(
networkx.maximum_flow_value(anal_graph, unit_anal_map[cur_port],
unified_out), capability_info,
ComponentInfo(cur_port, port_name_func(cur_port)))
def disjoint_paths_solution(path_to_graph: str, source: int, target: int) -> int:
""" Find the maximum amount of edge disjoint paths in graph from source to target
:param path_to_graph: path to the pickle file with the graph input
:param source: the desired source
:param target: the desired target
:return: maximum amount of disjoint paths
"""
"""
idea:
we will transfer the given graph into flow network, such that the capacity over every edge equals 1, and find the
maximum flow. we can show that the maximum flow (M) equals to the amount of edge disjoint paths in the graph (A):
A <= M:
let's set the flow to be 1 over every edge if it's part of any of the paths, else 0. this satisfy the capacity
constrain. this way, a unit of flow arrived the target through every such path, so the total flow is A.
therefore, the maximum flow is at least A.
M <= A:
using the integrality theorem (see mathematical section above), there exist a flow over the edges that uses only
integers. since our capacities are all ones, it means that the flow over every edge can be 0 or 1. it means there
are at least M edges leaving the source, each one has flow of 1.
now we use conservation:
for each of these edges, let's look at it's end-vertex. it must have an out-going edge with flow 1 (by conservation)
and it must be edge we haven't visited yet (to keep the capacity constrain). this way, for every edge with flow 1
leaving source, we can create a new edge-disjoint path from source to target, so there are at least M such paths.
so, A=M, and we should just find the maximal path.
"""
g = nx.read_gpickle(os.path.join(os.getcwd(), path_to_graph))
nx.set_edge_attributes(g, {edge: 1 for edge in g.edges}, 'capacity')
return nx.maximum_flow_value(g, source, target)
def getFlowGrouping(mat):
n = 20
shannonEntropies = [mat[i, i] for i in range(mat.shape[0])]
mat2 = sparsify(mat)
connectome = np.zeros((n, n))
for i in range(n):
for j in range(n):
#print("Nodes "+str(i)+" "+str(j)+".")
G = nx.DiGraph(data=np.multiply(mat2, lobe_group_masks[i, j]))
remove = [
node for node, degree in G.degree().items() if degree == 0
]
G.remove_nodes_from(remove)
flow = 0.0
original_nodes = G.nodes()
#H=capacitate(G,shannonEntropies)
for node1 in original_nodes:
for node2 in original_nodes:
if node1 != node2:
if node1 in lobe_map[i] and node2 in lobe_map[j]:
flow += nx.maximum_flow_value(G,
node1,
node2,
capacity='weight')
#flow+=nx.maximum_flow_value(H,str(node1)+'_in',str(node2)+'_out',capacity='weight')
connectome[i, j] = flow
return connectome
def test_disconnected(self):
G = nx.Graph()
G.add_weighted_edges_from([(0,1,1),(1,2,1),(2,3,1)],weight='capacity')
G.remove_node(1)
assert_equal(nx.maximum_flow_value(G,0,3), 0)
flowSoln = {0: {}, 2: {3: 0}, 3: {2: 0}}
compare_flows_and_cuts(G, 0, 3, flowSoln, 0)
def test_disconnected(self):
G = nx.Graph()
G.add_weighted_edges_from([(0, 1, 1), (1, 2, 1), (2, 3, 1)], weight='capacity')
G.remove_node(1)
assert nx.maximum_flow_value(G, 0, 3) == 0
flowSoln = {0: {}, 2: {3: 0}, 3: {2: 0}}
compare_flows_and_cuts(G, 0, 3, flowSoln, 0)
def FlowSum(graph):
sum = 0
#wanted to count only the vertix that has a path, another option is using the method "has_path"
flowDict = nx.all_pairs_shortest_path_length(graph)
for source in flowDict.keys():
for target in (flowDict[source]).keys():
sum += nx.maximum_flow_value(graph, source, target)
return sum / 2
class Topology(object, nx.Graph):
for N in [20, 30, 40]:
for delta in [2, 4, 8]:
fmax_vector = []
for i in range(5):
nodes = range(N)
np.random.seed(5)
degree = [delta for i in xrange(N)]
G = nx.directed_havel_hakimi_graph(degree, degree)
G = nx.DiGraph(G)
bb = nx.edge_betweenness_centrality(G, normalized=False)
nx.set_edge_attributes(G, 'weight', bb)
nx.set_edge_attributes(G, 'capacity', bb)
T_matrix = np.zeros((N, N))
for s in nodes:
for d in nodes:
if s != d:
flow = np.random.uniform(0.5, 1.5)
T_matrix[s, d] = flow
if G.has_edge(s, d):
G.edge[s][d]['weight'] = flow
G.edge[s][d]['capacity'] = np.random.randint(
8, 12)
f_value = 0
(p, a) = (0, 0)
for i in range(N):
for j in range(N):
edges = nx.shortest_path(G, i, j, weight='weight')
for k in range(len(edges) - 1):
G.edge[edges[k]][edges[
k + 1]]['weight'] += T_matrix[i][j]
if i != j:
flow_value = nx.maximum_flow_value(G, i, j)
if flow_value > f_value:
f_value = flow_value
(p, a) = (i, j)
fmax = 0
(s_f, d_f) = (0, 0)
for s in G.edge:
for d in G.edge[s]:
if G.edge[s][d]['weight'] > fmax:
fmax = G.edge[s][d]['weight']
(s_f, d_f) = (s, d)
fmax_vector.append(fmax)
tot_edges = G.number_of_edges()
np.set_printoptions(precision=3)
#print T_matrix
#print tot_edges
print 'N = ' + str(N) + ' D = ' + str(delta) + 'fmax = ' + str(
np.mean(fmax_vector)) #+ ' flow = ' + str(flow_value)
def disruption(G, originalMaxFlow, upstreamNodes, downstreamNodes):
"""
Calculate the disruption for each node in the graph.
This is done by removing the node, calculating the new flow, and
seeing how different that was from the original.
input: G, the graph
originalMaxFlow, the original maximum flow value
upstreamNodes, a list of the upstream nodes
downstreamNodes, a list of the downstream nodes
output: none, but prints the table of results to stdout
"""
#print("Total number of nodes in graph = ", nx.number_of_nodes(G))
print("Calculating Disruption... ")
disruptionDict = {'source': float('inf'), 'sink': float('inf')}
sortedGraph = sorted(G.nodes())
for node in sortedGraph:
if node != 'source' and node != 'sink':
outEdges = G.out_edges(node, data=True)
inEdges = G.in_edges(node, data=True)
G.remove_node(node)
try:
flow_value = nx.maximum_flow_value(G, 'source', 'sink')
flowDifference = originalMaxFlow - flow_value
disruptionDict[node] = flowDifference
except:
print(sys.exc_info()[0])
print("Error evaluating flow when removing node ", node)
sys.exit(1)
G.add_node(node)
G.add_edges_from(inEdges)
G.add_edges_from(outEdges)
nodes = G.nodes()
sortedDisruption = sorted(nodes, key=disruptionDict.__getitem__, reverse=True)
sortedDisruption.remove('source')
sortedDisruption.remove('sink')
zeroEffectGenes = ""
print("Flow Difference {0:2} % Change {1:8} Node type {2:2} Node ".format("","",""))
print('------------------------------------------------------------------')
for node in sortedDisruption:
flowDifference = disruptionDict[node]
percentChange = flowDifference / originalMaxFlow * 100
nodeType = "linker"
if node in upstreamNodes:
nodeType = "UPSTREAM"
elif node in downstreamNodes:
nodeType = "DOWNSTREAM"
if flowDifference <= 0.005:
zeroEffectGenes += node + "\t "
else:
print("{0:20} {1:15} {2:12} {3}".format('%.2f' % flowDifference,
'%.2f' % percentChange, nodeType, node))
# These were clogging up the output, so I condensed them a bit
print("\nGenes that had zero effect on flow: ")
print(zeroEffectGenes)
def test_complete_graph_cutoff(self):
G = nx.complete_graph(5)
nx.set_edge_attributes(G, {(u, v): 1 for u, v in G.edges()},
'capacity')
for flow_func in [shortest_augmenting_path, edmonds_karp]:
for cutoff in [3, 2, 1]:
result = nx.maximum_flow_value(G, 0, 4, flow_func=flow_func,
cutoff=cutoff)
assert cutoff == result, "cutoff error in {0}".format(flow_func.__name__)
def apply(net):
"""
Using the max-flow min-cut theorem, we compute a list of nett well handled TP and PT pairs
(T=transition, P=place)
:param net: Petri Net
:return: List
"""
graph, booking = create_network_graph(net)
pairs = []
for place in net.places:
for transition in net.transitions:
p = booking[place]
t = booking[transition]
if nx.maximum_flow_value(graph, p + 1, t) > 1:
pairs.append((p + 1, t))
if nx.maximum_flow_value(graph, t + 1, p) > 1:
pairs.append((t + 1, p))
return pairs
def main(N, adj, k, L):
iterations = 10
result = 'Failed'
while iterations > 0 and result == 'Failed':
print iterations
G = getGraph(N, adj)
S = getS(G, k)
S = doOneSwaps(G, S, L)
H = defaultdict(list)
result = None
#max flow value cannot be greater than the number of nodes in the graph or set V
if nx.maximum_flow_value(getFlowGraph(G, S, L), 's', 't') == N:
#uncomment the below to compute assignments
'''_,flows = nx.maximum_flow(getFlowGraph(G, S, L), 's', 't')
edges = set(G.edges())
#if a flow exists along a particular path assigning v to that vertex in S
for v in G.nodes():
for s in S:
if (min(v,s),max(v,s)) in edges:
unitflow = False
try:
if flows[max(v,s + N)][min(v,s + N)] == 1:
unitflow = True
except KeyError:
try:
if flows[min(v,s + N)][max(v,s + N)] == 1:
unitflow = True
except KeyError:
pass
if unitflow:
H[s].append(v)'''
result = 'Success'
else:
result = 'Failed'
iterations -= 1
if result == 'Failed':
''' Save the graph as an image, and its adjacency matrix
as a pickle file '''
pos = nx.spring_layout(G, k=0.5)
nx.draw_networkx_nodes(G,
pos,
nodelist=S,
node_color='b',
node_size=200)
nx.draw_networkx_nodes(G,
pos,
nodelist=list(set(G.nodes()) - set(S)),
node_color='r',
node_size=200)
nx.draw_networkx_edges(G, pos, edgeList=list(G.edges()))
fname = str(randint(1, 10**9))
plt.savefig('failures/' + fname)
a = [[0 for _ in xrange(N)] for _ in xrange(N)]
for key, val in adj.iteritems():
a[key[0]][key[1]] = val
pickle.dump(a, open('failures/' + fname, 'w'))
return result
def get_flow(self):
try:
R = nx.algorithms.flow.edmonds_karp(self.G, self.start, self.end)
flow_val = nx.maximum_flow_value(self.G, self.start, self.end)
if self.debug >= 2:
print("max_flow: " + str(flow_val))
print(flow_val == R.graph["flow_value"])
except nx.exception.NetworkXError:
print("self.G.nodes() is None")
def test_complete_graph_cutoff(self):
G = nx.complete_graph(5)
nx.set_edge_attributes(G, 'capacity',
dict(((u, v), 1) for u, v in G.edges()))
for flow_func in [shortest_augmenting_path, edmonds_karp]:
for cutoff in [3, 2, 1]:
result = nx.maximum_flow_value(G, 0, 4, flow_func=flow_func,
cutoff=cutoff)
assert_equal(cutoff, result,
msg="cutoff error in {0}".format(flow_func.__name__))
def MaxFlow(graph):
max = 0
#wanted to count only the vertix that has a path, another option is using the method "has_path"
flowDict = nx.all_pairs_shortest_path_length(graph)
for source in flowDict.keys():
for target in (flowDict[source]).keys():
flow = nx.maximum_flow_value(graph, source, target)
if (flow > max):
max = flow
return max / 2 #counts twice
def build_max_flows_dict(g):
global i, j
for i in g.nodes():
for j in g.nodes():
if i == j:
continue
# nice function in networkX to find the
# maximum flow in a single-commodity flow.
max_flows_dict[(i, j)] = nx.maximum_flow_value(g, i, j)
return max_flows_dict
def maxFlowValue(workers, taskids, b=1):
"""
Compute max-flow between source s and destination d
:param workers:
:param taskids:
:param b:
:return:
"""
DG = createDG(workers, taskids, b)
return nx.maximum_flow_value(DG, "s", "d")
def test_pyramid(self):
N = 10
# N = 100 # this gives a graph with 5051 nodes
G = gen_pyramid(N)
R = build_residual_network(G, "capacity")
kwargs = dict(residual=R)
for flow_func in flow_funcs:
kwargs["flow_func"] = flow_func
flow_value = nx.maximum_flow_value(G, (0, 0), "t", **kwargs)
assert_almost_equal(flow_value, 1.0, msg=msg.format(flow_func.__name__))
def test_complete_graph(self):
N = 50
G = nx.complete_graph(N)
nx.set_edge_attributes(G, 5, 'capacity')
R = build_residual_network(G, 'capacity')
kwargs = dict(residual=R)
for flow_func in flow_funcs:
kwargs['flow_func'] = flow_func
flow_value = nx.maximum_flow_value(G, 1, 2, **kwargs)
assert flow_value == 5 * (N - 1), msg.format(flow_func.__name__)
def test_complete_graph(self):
N = 50
G = nx.complete_graph(N)
nx.set_edge_attributes(G, "capacity", 5)
R = build_residual_network(G, "capacity")
kwargs = dict(residual=R)
for flow_func in flow_funcs:
kwargs["flow_func"] = flow_func
flow_value = nx.maximum_flow_value(G, 1, 2, **kwargs)
assert_equal(flow_value, 5 * (N - 1), msg=msg.format(flow_func.__name__))
def netflow_step(self):
for node in self.graph.nodes_iter():
if node == self.identity:
self.graph.node[node]['score'] = 0
continue
score = nx.maximum_flow_value(self.augmented_graph, node + "IN",
self.identity + "OUT")
self.graph.node[node]['score'] = score
def test_pyramid(self):
N = 10
# N = 100 # this gives a graph with 5051 nodes
G = gen_pyramid(N)
R = build_residual_network(G, 'capacity')
kwargs = dict(residual=R)
for flow_func in flow_funcs:
kwargs['flow_func'] = flow_func
flow_value = nx.maximum_flow_value(G, (0, 0), 't', **kwargs)
assert almost_equal(flow_value, 1.), msg.format(flow_func.__name__)
def find_maximum_flow(H, s, t):
'''Finds maximum flow between a source and target node in DiGraph G.
Requires edge attribute 'capacity'. MultiDiGraphs not supported.
'''
if type(H) == nx.classes.digraph.DiGraph:
max_flow_path = nx.maximum_flow(H, s, t)
max_flow = nx.maximum_flow_value(H, s, t)
return max_flow_path, max_flow
else:
raise TypeError('Graph must be DiGraph type. Use \
convert_to_digraph to help convert a MultiDiGraph to a DiGraph, \
which may result in loss of information')
def get_max_flow_demand(G):
results = []
max_flow = 0
for i in G:
for j in G:
if (i == j):
continue
else:
flow = nx.maximum_flow_value(G, i, j)
flow = int(flow)
results.append(flow)
return results
def test_pyramid(self):
N = 10
# N = 100 # this gives a graph with 5051 nodes
G = gen_pyramid(N)
R = build_residual_network(G, "capacity")
kwargs = dict(residual=R)
for flow_func in flow_funcs:
kwargs["flow_func"] = flow_func
errmsg = f"Assertion failed in function: {flow_func.__name__}"
flow_value = nx.maximum_flow_value(G, (0, 0), "t", **kwargs)
assert almost_equal(flow_value, 1.0), errmsg
def test_complete_graph(self):
N = 50
G = nx.complete_graph(N)
nx.set_edge_attributes(G, 5, "capacity")
R = build_residual_network(G, "capacity")
kwargs = dict(residual=R)
for flow_func in flow_funcs:
kwargs["flow_func"] = flow_func
errmsg = f"Assertion failed in function: {flow_func.__name__}"
flow_value = nx.maximum_flow_value(G, 1, 2, **kwargs)
assert flow_value == 5 * (N - 1), errmsg
def find_max_flow(good_routes, ny, sf, plane_cap, draw=False):
matrix, sink_index, v_map = create_adj_matrix(good_routes,
plane_cap,
ny,
sf,
draw=draw)
graph = nx.convert_matrix.from_numpy_matrix(matrix,
create_using=nx.DiGraph)
return nx.maximum_flow_value(graph,
len(matrix) - 1,
sink_index,
capacity='weight')
def max_congestion(G):
num_of_nodes = G.number_of_nodes()
max_value = 1
for x in range(num_of_nodes):
if G.degree(x) <= max_value:
break
else:
for y in range(x + 1, num_of_nodes):
current_value = nx.maximum_flow_value(G, x, y)
if max_value < current_value:
max_value = current_value
print(max_value)
def __faultScen_single_edge(self):
edgeFaultEffectonFlow = {}
faultyEdgeFlow = {}
for e in self.G.edges:
g = self.G.copy()
g[e[0]][e[1]]['capacity'] = 0
_, edgeFaultEffectonFlow[e], _ = self.maxFlowMinCost(g)
faultyEdgeFlow[e] = nx.maximum_flow_value(g, _s='s', _t='t')
faultDF = pd.DataFrame.from_dict(edgeFaultEffectonFlow)
faultDF.set_index(faultDF.index.values, inplace=True)
faultDF.columns = faultDF.columns.values
return faultDF, faultyEdgeFlow, edgeFaultEffectonFlow
def cli(ek, draw, input_file):
g, source, sink = parse_dicaps_graph(input_file)
if draw:
write_dot(g, 'graph.dot')
return
if ek:
print('Using Edmonds Karp')
flow_func = edmonds_karp
else:
print('Using Preflow Push')
flow_func = None
t0 = time.time()
flow = nx.maximum_flow_value(g, source, sink, flow_func=flow_func)
t1 = time.time()
print("Max Flow Solution: {0}".format(flow))
print("Runtime: {0}s".format(t1 - t0))
def person_max_flow(graph, num_strategic, sybil_pct=0, cutlinks=True,
gensybils=True, strategic_agents=None,
return_data=False):
graph = graph.copy()
N = graph.number_of_nodes()
if strategic_agents is None:
strategic_agents = random_strategic_agents(graph, num_strategic)
saved_edges = {}
if cutlinks:
saved_edges = {a: graph.edges(a, data=True) for a in strategic_agents}
cut_outlinks(graph, strategic_agents, leave_one=True) # TODO: Are you sure you want leave_one=True?
after_edges = {a: graph.edges(a, data=True) for a in strategic_agents}
# For Max Flow, don't apply sybils since it is strategyproof to sybils
# if gensybils:
# num_sybils = int(graph.number_of_nodes() * sybil_pct)
# generate_sybils(graph, strategic_agents, num_sybils)
# Need to reimplement max flow here because we only want to cut outedges
# When we're not being evaluated.
scores = np.zeros((N, N))
for i in xrange(N):
# Add back in the edges for this agent, so we can get an actual score.
# if cutlinks and i in strategic_agents:
# graph.remove_edges_from(graph.edges(i))
# graph.add_edges_from(saved_edges[i])
# Now compute the max flow scores
for j in xrange(N):
if i != j:
scores[i, j] = nx.maximum_flow_value(graph, i, j, capacity='weight')
# scores[i, j] = utils.fast_max_flow(graph.gt_graph, i, j)
# Restore post-cut edges
# if cutlinks and i in strategic_agents:
# graph.remove_edges_from(graph.edges(i))
# graph.add_edges_from(after_edges[i])
sys.stdout.write('.')
sys.stdout.write("\n")
if return_data:
return scores, {'strategic_agents': strategic_agents, 'graph': graph}
else:
return scores
def getStartingWeights(G, numNodes, unipartite): if unipartite == True: weights=numpy.zeros((numNodes,numNodes)) for edge in G.edges(): source = edge[0] dest = edge[1] flow = nx.maximum_flow_value(G, source, dest) weights[source][dest] = flow weights[dest][source] = flow else: shortestPaths=nx.all_pairs_shortest_path_length(G) weights=numpy.zeros((numNodes,numNodes)) for sourceNode,paths in shortestPaths.items(): for destNode,pathLength in paths.items(): weights[sourceNode][destNode]=pathLength Y = squareform(weights) return Y
def CalMaxFlows(DG_network, Dnodes, maxFlows): """ If two nodes are connected in networkx graph G, This function returns maxflow value, shortest path length, minimum edges cut between this two nodes. """ for i in range(len(Dnodes)): for j in range(i+1, len(Dnodes)): if nx.has_path(DG_network, Dnodes[i], Dnodes[j]): maxflow = nx.maximum_flow_value(DG_network, Dnodes[i], Dnodes[j], capacity = 'weight') shortest_path_length = nx.shortest_path_length(DG_network, source = Dnodes[i], target = Dnodes[j]) min_edges_cut = len(nx.minimum_edge_cut(DG_network, Dnodes[i], Dnodes[j])) else: continue if Dnodes[i] < Dnodes[j]: a_path = (Dnodes[i], Dnodes[j]) else: a_path = (Dnodes[j], Dnodes[i]) if not maxFlows.has_key(a_path): maxFlows[a_path] = (maxflow, shortest_path_length, min_edges_cut) else: print "impossibly!", a_path sys.exit(1)
def local_edge_connectivity(G, u, v, flow_func=None, auxiliary=None,
residual=None, cutoff=None):
r"""Returns local edge connectivity for nodes s and t in G.
Local edge connectivity for two nodes s and t is the minimum number
of edges that must be removed to disconnect them.
This is a flow based implementation of edge connectivity. We compute the
maximum flow on an auxiliary digraph build from the original
network (see below for details). This is equal to the local edge
connectivity because the value of a maximum s-t-flow is equal to the
capacity of a minimum s-t-cut (Ford and Fulkerson theorem) [1]_ .
Parameters
----------
G : NetworkX graph
Undirected or directed graph
s : node
Source node
t : node
Target node
flow_func : function
A function for computing the maximum flow among a pair of nodes.
The function has to accept at least three parameters: a Digraph,
a source node, and a target node. And return a residual network
that follows NetworkX conventions (see :meth:`maximum_flow` for
details). If flow_func is None, the default maximum flow function
(:meth:`edmonds_karp`) is used. See below for details. The
choice of the default function may change from version
to version and should not be relied on. Default value: None.
auxiliary : NetworkX DiGraph
Auxiliary digraph for computing flow based edge connectivity. If
provided it will be reused instead of recreated. Default value: None.
residual : NetworkX DiGraph
Residual network to compute maximum flow. If provided it will be
reused instead of recreated. Default value: None.
cutoff : integer, float
If specified, the maximum flow algorithm will terminate when the
flow value reaches or exceeds the cutoff. This is only for the
algorithms that support the cutoff parameter: :meth:`edmonds_karp`
and :meth:`shortest_augmenting_path`. Other algorithms will ignore
this parameter. Default value: None.
Returns
-------
K : integer
local edge connectivity for nodes s and t.
Examples
--------
This function is not imported in the base NetworkX namespace, so you
have to explicitly import it from the connectivity package:
>>> from networkx.algorithms.connectivity import local_edge_connectivity
We use in this example the platonic icosahedral graph, which has edge
connectivity 5.
>>> G = nx.icosahedral_graph()
>>> local_edge_connectivity(G, 0, 6)
5
If you need to compute local connectivity on several pairs of
nodes in the same graph, it is recommended that you reuse the
data structures that NetworkX uses in the computation: the
auxiliary digraph for edge connectivity, and the residual
network for the underlying maximum flow computation.
Example of how to compute local edge connectivity among
all pairs of nodes of the platonic icosahedral graph reusing
the data structures.
>>> import itertools
>>> # You also have to explicitly import the function for
>>> # building the auxiliary digraph from the connectivity package
>>> from networkx.algorithms.connectivity import (
... build_auxiliary_edge_connectivity)
>>> H = build_auxiliary_edge_connectivity(G)
>>> # And the function for building the residual network from the
>>> # flow package
>>> from networkx.algorithms.flow import build_residual_network
>>> # Note that the auxiliary digraph has an edge attribute named capacity
>>> R = build_residual_network(H, 'capacity')
>>> result = dict.fromkeys(G, dict())
>>> # Reuse the auxiliary digraph and the residual network by passing them
>>> # as parameters
>>> for u, v in itertools.combinations(G, 2):
... k = local_edge_connectivity(G, u, v, auxiliary=H, residual=R)
... result[u][v] = k
>>> all(result[u][v] == 5 for u, v in itertools.combinations(G, 2))
True
You can also use alternative flow algorithms for computing edge
connectivity. For instance, in dense networks the algorithm
:meth:`shortest_augmenting_path` will usually perform better than
the default :meth:`edmonds_karp` which is faster for sparse
networks with highly skewed degree distributions. Alternative flow
functions have to be explicitly imported from the flow package.
>>> from networkx.algorithms.flow import shortest_augmenting_path
>>> local_edge_connectivity(G, 0, 6, flow_func=shortest_augmenting_path)
5
Notes
-----
This is a flow based implementation of edge connectivity. We compute the
maximum flow using, by default, the :meth:`edmonds_karp` algorithm on an
auxiliary digraph build from the original input graph:
If the input graph is undirected, we replace each edge (`u`,`v`) with
two reciprocal arcs (`u`, `v`) and (`v`, `u`) and then we set the attribute
'capacity' for each arc to 1. If the input graph is directed we simply
add the 'capacity' attribute. This is an implementation of algorithm 1
in [1]_.
The maximum flow in the auxiliary network is equal to the local edge
connectivity because the value of a maximum s-t-flow is equal to the
capacity of a minimum s-t-cut (Ford and Fulkerson theorem).
See also
--------
:meth:`edge_connectivity`
:meth:`local_node_connectivity`
:meth:`node_connectivity`
:meth:`maximum_flow`
:meth:`edmonds_karp`
:meth:`preflow_push`
:meth:`shortest_augmenting_path`
References
----------
.. [1] Abdol-Hossein Esfahanian. Connectivity Algorithms.
http://www.cse.msu.edu/~cse835/Papers/Graph_connectivity_revised.pdf
"""
if flow_func is None:
flow_func = default_flow_func
if auxiliary is None:
H = build_auxiliary_edge_connectivity(G)
else:
H = auxiliary
kwargs = dict(flow_func=flow_func, residual=residual)
if flow_func is shortest_augmenting_path:
kwargs['cutoff'] = cutoff
kwargs['two_phase'] = True
elif flow_func is edmonds_karp:
kwargs['cutoff'] = cutoff
return nx.maximum_flow_value(H, u, v, **kwargs)
def local_node_connectivity(G, s, t, flow_func=None, auxiliary=None,
residual=None, cutoff=None):
r"""Computes local node connectivity for nodes s and t.
Local node connectivity for two non adjacent nodes s and t is the
minimum number of nodes that must be removed (along with their incident
edges) to disconnect them.
This is a flow based implementation of node connectivity. We compute the
maximum flow on an auxiliary digraph build from the original input
graph (see below for details).
Parameters
----------
G : NetworkX graph
Undirected graph
s : node
Source node
t : node
Target node
flow_func : function
A function for computing the maximum flow among a pair of nodes.
The function has to accept at least three parameters: a Digraph,
a source node, and a target node. And return a residual network
that follows NetworkX conventions (see :meth:`maximum_flow` for
details). If flow_func is None, the default maximum flow function
(:meth:`edmonds_karp`) is used. See below for details. The choice
of the default function may change from version to version and
should not be relied on. Default value: None.
auxiliary : NetworkX DiGraph
Auxiliary digraph to compute flow based node connectivity. It has
to have a graph attribute called mapping with a dictionary mapping
node names in G and in the auxiliary digraph. If provided
it will be reused instead of recreated. Default value: None.
residual : NetworkX DiGraph
Residual network to compute maximum flow. If provided it will be
reused instead of recreated. Default value: None.
cutoff : integer, float
If specified, the maximum flow algorithm will terminate when the
flow value reaches or exceeds the cutoff. This is only for the
algorithms that support the cutoff parameter: :meth:`edmonds_karp`
and :meth:`shortest_augmenting_path`. Other algorithms will ignore
this parameter. Default value: None.
Returns
-------
K : integer
local node connectivity for nodes s and t
Examples
--------
This function is not imported in the base NetworkX namespace, so you
have to explicitly import it from the connectivity package:
>>> from networkx.algorithms.connectivity import local_node_connectivity
We use in this example the platonic icosahedral graph, which has node
connectivity 5.
>>> G = nx.icosahedral_graph()
>>> local_node_connectivity(G, 0, 6)
5
If you need to compute local connectivity on several pairs of
nodes in the same graph, it is recommended that you reuse the
data structures that NetworkX uses in the computation: the
auxiliary digraph for node connectivity, and the residual
network for the underlying maximum flow computation.
Example of how to compute local node connectivity among
all pairs of nodes of the platonic icosahedral graph reusing
the data structures.
>>> import itertools
>>> # You also have to explicitly import the function for
>>> # building the auxiliary digraph from the connectivity package
>>> from networkx.algorithms.connectivity import (
... build_auxiliary_node_connectivity)
...
>>> H = build_auxiliary_node_connectivity(G)
>>> # And the function for building the residual network from the
>>> # flow package
>>> from networkx.algorithms.flow import build_residual_network
>>> # Note that the auxiliary digraph has an edge attribute named capacity
>>> R = build_residual_network(H, 'capacity')
>>> result = dict.fromkeys(G, dict())
>>> # Reuse the auxiliary digraph and the residual network by passing them
>>> # as parameters
>>> for u, v in itertools.combinations(G, 2):
... k = local_node_connectivity(G, u, v, auxiliary=H, residual=R)
... result[u][v] = k
...
>>> all(result[u][v] == 5 for u, v in itertools.combinations(G, 2))
True
You can also use alternative flow algorithms for computing node
connectivity. For instance, in dense networks the algorithm
:meth:`shortest_augmenting_path` will usually perform better than
the default :meth:`edmonds_karp` which is faster for sparse
networks with highly skewed degree distributions. Alternative flow
functions have to be explicitly imported from the flow package.
>>> from networkx.algorithms.flow import shortest_augmenting_path
>>> local_node_connectivity(G, 0, 6, flow_func=shortest_augmenting_path)
5
Notes
-----
This is a flow based implementation of node connectivity. We compute the
maximum flow using, by default, the :meth:`edmonds_karp` algorithm (see:
:meth:`maximum_flow`) on an auxiliary digraph build from the original
input graph:
For an undirected graph G having `n` nodes and `m` edges we derive a
directed graph H with `2n` nodes and `2m+n` arcs by replacing each
original node `v` with two nodes `v_A`, `v_B` linked by an (internal)
arc in H. Then for each edge (`u`, `v`) in G we add two arcs
(`u_B`, `v_A`) and (`v_B`, `u_A`) in H. Finally we set the attribute
capacity = 1 for each arc in H [1]_ .
For a directed graph G having `n` nodes and `m` arcs we derive a
directed graph H with `2n` nodes and `m+n` arcs by replacing each
original node `v` with two nodes `v_A`, `v_B` linked by an (internal)
arc (`v_A`, `v_B`) in H. Then for each arc (`u`, `v`) in G we add one arc
(`u_B`, `v_A`) in H. Finally we set the attribute capacity = 1 for
each arc in H.
This is equal to the local node connectivity because the value of
a maximum s-t-flow is equal to the capacity of a minimum s-t-cut.
See also
--------
:meth:`local_edge_connectivity`
:meth:`node_connectivity`
:meth:`minimum_node_cut`
:meth:`maximum_flow`
:meth:`edmonds_karp`
:meth:`preflow_push`
:meth:`shortest_augmenting_path`
References
----------
.. [1] Kammer, Frank and Hanjo Taubig. Graph Connectivity. in Brandes and
Erlebach, 'Network Analysis: Methodological Foundations', Lecture
Notes in Computer Science, Volume 3418, Springer-Verlag, 2005.
http://www.informatik.uni-augsburg.de/thi/personen/kammer/Graph_Connectivity.pdf
"""
if flow_func is None:
flow_func = default_flow_func
if auxiliary is None:
H = build_auxiliary_node_connectivity(G)
else:
H = auxiliary
mapping = H.graph.get('mapping', None)
if mapping is None:
raise nx.NetworkXError('Invalid auxiliary digraph.')
kwargs = dict(flow_func=flow_func, residual=residual)
if flow_func is shortest_augmenting_path:
kwargs['cutoff'] = cutoff
kwargs['two_phase'] = True
elif flow_func is edmonds_karp:
kwargs['cutoff'] = cutoff
return nx.maximum_flow_value(H, '%sB' % mapping[s], '%sA' % mapping[t], **kwargs)
global target
if len(sys.argv) != 4:
print "Usage: python <source_file> <path_of_input_data_file> <source_node> <sink_node> "
sys.exit()
else:
inputpath = sys.argv[1]
source = int(sys.argv[2])
target = int(sys.argv[3])
if __name__ == "__main__":
main(sys.argv)
#G=nx.read_gml("C:\Users\Justin\Documents\karate (1)\karate.gml")
G=nx.read_gml(inputpath)
for u in G.edges():
G[u[0]][u[1]]['capacity']=1.0
maxflow1= nx.maximum_flow_value(G,source,target)
mincut1 = nx.minimum_cut_value(G,source,target)
#H=nx.read_gml("C:\Users\Justin\Downloads\power\power.gml")
#for u in H.edges():
# H[u[0]][u[1]]['capacity']=1.0
#maxflow2 = nx.maximum_flow_value(H,2553,4458)
#mincut2 = nx.minimum_cut_value(H,2553,4458)
#print maxflow1, mincut1, maxflow2, mincut2
print maxflow1, mincut1
def local_node_connectivity(G, s, t, aux_digraph=None, mapping=None):
r"""Computes local node connectivity for nodes s and t.
Local node connectivity for two non adjacent nodes s and t is the
minimum number of nodes that must be removed (along with their incident
edges) to disconnect them.
This is a flow based implementation of node connectivity. We compute the
maximum flow on an auxiliary digraph build from the original input
graph (see below for details). This is equal to the local node
connectivity because the value of a maximum s-t-flow is equal to the
capacity of a minimum s-t-cut (Ford and Fulkerson theorem) [1]_ .
Parameters
----------
G : NetworkX graph
Undirected graph
s : node
Source node
t : node
Target node
aux_digraph : NetworkX DiGraph (default=None)
Auxiliary digraph to compute flow based node connectivity. If None
the auxiliary digraph is build.
mapping : dict (default=None)
Dictionary with a mapping of node names in G and in the auxiliary digraph.
Returns
-------
K : integer
local node connectivity for nodes s and t
Examples
--------
>>> # Platonic icosahedral graph has node connectivity 5
>>> # for each non adjacent node pair
>>> G = nx.icosahedral_graph()
>>> nx.local_node_connectivity(G,0,6)
5
Notes
-----
This is a flow based implementation of node connectivity. We compute the
maximum flow using the Ford and Fulkerson algorithm on an auxiliary digraph
build from the original input graph:
For an undirected graph G having `n` nodes and `m` edges we derive a
directed graph D with 2n nodes and 2m+n arcs by replacing each
original node `v` with two nodes `v_A`, `v_B` linked by an (internal)
arc in `D`. Then for each edge (`u`, `v`) in G we add two arcs
(`u_B`, `v_A`) and (`v_B`, `u_A`) in `D`. Finally we set the attribute
capacity = 1 for each arc in `D` [1]_ .
For a directed graph G having `n` nodes and `m` arcs we derive a
directed graph `D` with `2n` nodes and `m+n` arcs by replacing each
original node `v` with two nodes `v_A`, `v_B` linked by an (internal)
arc `(v_A, v_B)` in D. Then for each arc `(u,v)` in G we add one arc
`(u_B,v_A)` in `D`. Finally we set the attribute capacity = 1 for
each arc in `D`.
This is equal to the local node connectivity because the value of
a maximum s-t-flow is equal to the capacity of a minimum s-t-cut (Ford
and Fulkerson theorem).
See also
--------
node_connectivity
all_pairs_node_connectivity_matrix
local_edge_connectivity
edge_connectivity
max_flow
ford_fulkerson
References
----------
.. [1] Kammer, Frank and Hanjo Taubig. Graph Connectivity. in Brandes and
Erlebach, 'Network Analysis: Methodological Foundations', Lecture
Notes in Computer Science, Volume 3418, Springer-Verlag, 2005.
http://www.informatik.uni-augsburg.de/thi/personen/kammer/Graph_Connectivity.pdf
"""
if aux_digraph is None or mapping is None:
H, mapping = _aux_digraph_node_connectivity(G)
else:
H = aux_digraph
return nx.maximum_flow_value(H,'%sB' % mapping[s], '%sA' % mapping[t])
def local_edge_connectivity(G, u, v, aux_digraph=None):
r"""Returns local edge connectivity for nodes s and t in G.
Local edge connectivity for two nodes s and t is the minimum number
of edges that must be removed to disconnect them.
This is a flow based implementation of edge connectivity. We compute the
maximum flow on an auxiliary digraph build from the original
network (see below for details). This is equal to the local edge
connectivity because the value of a maximum s-t-flow is equal to the
capacity of a minimum s-t-cut (Ford and Fulkerson theorem) [1]_ .
Parameters
----------
G : NetworkX graph
Undirected or directed graph
s : node
Source node
t : node
Target node
aux_digraph : NetworkX DiGraph (default=None)
Auxiliary digraph to compute flow based edge connectivity. If None
the auxiliary digraph is build.
Returns
-------
K : integer
local edge connectivity for nodes s and t
Examples
--------
>>> # Platonic icosahedral graph has edge connectivity 5
>>> # for each non adjacent node pair
>>> G = nx.icosahedral_graph()
>>> nx.local_edge_connectivity(G,0,6)
5
Notes
-----
This is a flow based implementation of edge connectivity. We compute the
maximum flow using the Ford and Fulkerson algorithm on an auxiliary digraph
build from the original graph:
If the input graph is undirected, we replace each edge (u,v) with
two reciprocal arcs `(u,v)` and `(v,u)` and then we set the attribute
'capacity' for each arc to 1. If the input graph is directed we simply
add the 'capacity' attribute. This is an implementation of algorithm 1
in [1]_.
The maximum flow in the auxiliary network is equal to the local edge
connectivity because the value of a maximum s-t-flow is equal to the
capacity of a minimum s-t-cut (Ford and Fulkerson theorem).
See also
--------
local_node_connectivity
node_connectivity
edge_connectivity
max_flow
ford_fulkerson
References
----------
.. [1] Abdol-Hossein Esfahanian. Connectivity Algorithms.
http://www.cse.msu.edu/~cse835/Papers/Graph_connectivity_revised.pdf
"""
if aux_digraph is None:
H = _aux_digraph_edge_connectivity(G)
else:
H = aux_digraph
return nx.maximum_flow_value(H, u, v)
def max_flow_min_cost(G, s, t, capacity='capacity', weight='weight'):
"""Return a maximum (s, t)-flow of minimum cost.
G is a digraph with edge costs and capacities. There is a source
node s and a sink node t. This function finds a maximum flow from
s to t whose total cost is minimized.
Parameters
----------
G : NetworkX graph
DiGraph on which a minimum cost flow satisfying all demands is
to be found.
s: node label
Source of the flow.
t: node label
Destination of 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'.
weight: string
Edges of the graph G are expected to have an attribute weight
that indicates the cost incurred by sending one unit of flow on
that edge. If not present, the weight is considered to be 0.
Default value: 'weight'.
Returns
-------
flowDict: dictionary
Dictionary of dictionaries keyed by nodes such that
flowDict[u][v] is the flow edge (u, v).
Raises
------
NetworkXError
This exception is raised if the input graph is not directed or
not connected.
NetworkXUnbounded
This exception is raised if there is an infinite capacity path
from s to t in G. In this case there is no maximum flow. This
exception is also raised if the digraph G has a cycle of
negative cost and infinite capacity. Then, the cost of a flow
is unbounded below.
See also
--------
cost_of_flow, min_cost_flow, min_cost_flow_cost, network_simplex
Notes
-----
This algorithm is not guaranteed to work if edge weights or demands
are floating point numbers (overflows and roundoff errors can
cause problems). As a workaround you can use integer numbers by
multiplying the relevant edge attributes by a convenient
constant factor (eg 100).
Examples
--------
>>> G = nx.DiGraph()
>>> G.add_edges_from([(1, 2, {'capacity': 12, 'weight': 4}),
... (1, 3, {'capacity': 20, 'weight': 6}),
... (2, 3, {'capacity': 6, 'weight': -3}),
... (2, 6, {'capacity': 14, 'weight': 1}),
... (3, 4, {'weight': 9}),
... (3, 5, {'capacity': 10, 'weight': 5}),
... (4, 2, {'capacity': 19, 'weight': 13}),
... (4, 5, {'capacity': 4, 'weight': 0}),
... (5, 7, {'capacity': 28, 'weight': 2}),
... (6, 5, {'capacity': 11, 'weight': 1}),
... (6, 7, {'weight': 8}),
... (7, 4, {'capacity': 6, 'weight': 6})])
>>> mincostFlow = nx.max_flow_min_cost(G, 1, 7)
>>> mincost = nx.cost_of_flow(G, mincostFlow)
>>> mincost
373
>>> from networkx.algorithms.flow import maximum_flow
>>> maxFlow = maximum_flow(G, 1, 7)[1]
>>> nx.cost_of_flow(G, maxFlow) >= mincost
True
>>> mincostFlowValue = (sum((mincostFlow[u][7] for u in G.predecessors(7)))
... - sum((mincostFlow[7][v] for v in G.successors(7))))
>>> mincostFlowValue == nx.maximum_flow_value(G, 1, 7)
True
"""
maxFlow = nx.maximum_flow_value(G, s, t, capacity=capacity)
H = nx.DiGraph(G)
H.add_node(s, demand=-maxFlow)
H.add_node(t, demand=maxFlow)
return min_cost_flow(H, capacity=capacity, weight=weight)
import math
import itertools as it
import networkx as nx
from networkx import DiGraph
for g in range(1, int(input()) + 1):
N, M = map(int, input().split())
stars = [input().strip() for _ in range(N)]
donors = {donor: list(favs) for donor, favs in map(lambda x: (x[0], x[1:]), (input().strip().split() for _ in range(M))) if len(favs) > 0}
L = math.ceil(sum(1 for _ in filter(lambda x: len(x) > 0, donors.values())) / N)
G = DiGraph()
for donor, favs in donors.items():
G.add_edge(0, donor, capacity=1)
for fav in favs:
G.add_edge(donor, fav)
for l in it.count(L):
for star in stars:
G.add_edge(star, 1, capacity=l)
if nx.maximum_flow_value(G, 0, 1) == len(donors):
print('Event {}:'.format(g), l)
break
for star in stars:
G.remove_edge(star, 1)
import networkx as nx
from networkx.algorithms.flow import shortest_augmenting_path
G = nx.DiGraph()
G.add_edge('x','a', capacity=100)
G.add_edge('x','b', capacity=100)
G.add_edge('a','c', capacity=100)
G.add_edge('b','c', capacity=100)
G.add_edge('b','d', capacity=100)
G.add_edge('d','e', capacity=100)
G.add_edge('c','y', capacity=100)
G.add_edge('e','y', capacity=100)
R = shortest_augmenting_path(G, 'x', 'y')
flow_value = nx.maximum_flow_value(G, 'x', 'y')
print flow_value
print flow_value == R.graph['flow_value']
def print_flow(flow):
for edge in G.edges():
n1, n2 = edge
print edge, flow[n1][n2]
print 'Flow value =', flow_value
print 'Flow ='
print_flow(maximum_flow)
# The maximum flow should equal the minimum cut.
# In[5]:
max_flow_value = nx.maximum_flow_value(G, 's', 't')
min_cut_value = nx.minimum_cut_value(G, 's', 't')
print max_flow_value == min_cut_value
# ## Flows with Demands
#
# Let's now record a demand value at each node (negative demand corresponds to supply at a node).
# In[6]:
# to add a property to a node, you should use G.node['s'] rather than
# G['s'] to reference the node.
G.node['s']['demand'] = -25
