Python networkx.maximum_flow_value函数代码示例

 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_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 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, "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 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 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)

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 

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])

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)

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)

#.........这里部分代码省略.........

    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)

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']