Python networkx.dijkstra_predecessor_and_distance() Examples

def test_dijkstra_predecessor(self):
        G = nx.path_graph(4)
        assert_equal(nx.dijkstra_predecessor_and_distance(G, 0),
                     ({0: [], 1: [0], 2: [1], 3: [2]}, {0: 0, 1: 1, 2: 2, 3: 3}))
        G = nx.grid_2d_graph(2, 2)
        pred, dist = nx.dijkstra_predecessor_and_distance(G, (0, 0))
        assert_equal(sorted(pred.items()),
                     [((0, 0), []), ((0, 1), [(0, 0)]),
                      ((1, 0), [(0, 0)]), ((1, 1), [(0, 1), (1, 0)])])
        assert_equal(sorted(dist.items()),
                     [((0, 0), 0), ((0, 1), 1), ((1, 0), 1), ((1, 1), 2)])

        XG = nx.DiGraph()
        XG.add_weighted_edges_from([('s', 'u', 10), ('s', 'x', 5),
                                    ('u', 'v', 1), ('u', 'x', 2),
                                    ('v', 'y', 1), ('x', 'u', 3),
                                    ('x', 'v', 5), ('x', 'y', 2),
                                    ('y', 's', 7), ('y', 'v', 6)])
        (P, D) = nx.dijkstra_predecessor_and_distance(XG, 's')
        assert_equal(P['v'], ['u'])
        assert_equal(D['v'], 9)
        (P, D) = nx.dijkstra_predecessor_and_distance(XG, 's', cutoff=8)
        assert_false('v' in D) 

def calculate_pressure_loss_critical_path(dP_timestep, thermal_network):
    dP_all_edges = dP_timestep[0]
    plant_node = thermal_network.all_nodes_df[thermal_network.all_nodes_df['Type'] == 'PLANT'].index[0]
    if max(dP_all_edges) > 0.0:
        pressure_losses_in_critical_paths = np.zeros(len(dP_all_edges))  # initialize array
        G = nx.Graph() # initial networkx
        G.add_nodes_from(thermal_network.all_nodes_df.index)
        for ix, edge_name in enumerate(thermal_network.edge_df.index):
            start_node = thermal_network.edge_df.loc[edge_name, 'start node']
            end_node = thermal_network.edge_df.loc[edge_name, 'end node']
            dP_one_edge = dP_all_edges[ix]
            G.add_edge(start_node, end_node, weight=dP_one_edge, name=edge_name, ix=str(ix))
        # find the path with the highest pressure drop
        _, distances_dict = nx.dijkstra_predecessor_and_distance(G, source=plant_node)
        critical_node = max(distances_dict, key=distances_dict.get)
        path_to_critical_node = nx.shortest_path(G, source=plant_node)[critical_node]
        # calculate pressure losses along the critical path
        for i in range(len(path_to_critical_node)):
            if i < len(path_to_critical_node) - 1:
                start_node = path_to_critical_node[i]
                end_node = path_to_critical_node[i+1]
                dP = G[start_node][end_node]['weight']
                idx = int(G[start_node][end_node]['ix'])
                pressure_losses_in_critical_paths[idx] = dP
        # find substations
        substation_nodes_ix = []
        node_df = thermal_network.all_nodes_df
        for node in path_to_critical_node:
            if node_df.ix[node]['Type'] != 'NONE':
                substation_nodes_ix.append(int(node.split('NODE')[1]))
    else:
        pressure_losses_in_critical_paths = np.zeros(len(dP_all_edges))  # zero array
        substation_nodes_ix = []

    return pressure_losses_in_critical_paths, substation_nodes_ix 

def test_dijkstra_pred_distance_multigraph(self):
        G = nx.MultiGraph()
        G.add_edge('a', 'b', key='short', foo=5, weight=100)
        G.add_edge('a', 'b', key='long', bar=1, weight=110)
        p, d = nx.dijkstra_predecessor_and_distance(G, 'a')
        assert_equal(p, {'a': [], 'b': ['a']})
        assert_equal(d, {'a': 0, 'b': 100}) 

def test_negative_edge_cycle(self):
        G = nx.cycle_graph(5, create_using=nx.DiGraph())
        assert_equal(nx.negative_edge_cycle(G), False)
        G.add_edge(8, 9, weight=-7)
        G.add_edge(9, 8, weight=3)
        graph_size = len(G)
        assert_equal(nx.negative_edge_cycle(G), True)
        assert_equal(graph_size, len(G))
        assert_raises(ValueError, nx.single_source_dijkstra_path_length, G, 8)
        assert_raises(ValueError, nx.single_source_dijkstra, G, 8)
        assert_raises(ValueError, nx.dijkstra_predecessor_and_distance, G, 8)
        G.add_edge(9, 10)
        assert_raises(ValueError, nx.bidirectional_dijkstra, G, 8, 10) 

def test_absent_source(self):
        # the check is in _dijkstra_multisource, but this will provide
        # regression testing against later changes to any of the "client"
        # Dijkstra or Bellman-Ford functions
        G = nx.path_graph(2)
        for fn in (nx.dijkstra_path,
                   nx.dijkstra_path_length,
                   nx.single_source_dijkstra_path,
                   nx.single_source_dijkstra_path_length,
                   nx.single_source_dijkstra,
                   nx.dijkstra_predecessor_and_distance,):
            assert_raises(nx.NodeNotFound, fn, G, 3, 0) 

def test_dijkstra_predecessor1(self):
        G = nx.path_graph(4)
        assert_equal(nx.dijkstra_predecessor_and_distance(G, 0),
                     ({0: [], 1: [0], 2: [1], 3: [2]}, {0: 0, 1: 1, 2: 2, 3: 3})) 

def test_dijkstra_predecessor2(self):
        # 4-cycle
        G = nx.Graph([(0, 1), (1, 2), (2, 3), (3, 0)])
        pred, dist = nx.dijkstra_predecessor_and_distance(G, (0))
        assert_equal(pred[0], [])
        assert_equal(pred[1], [0])
        assert_true(pred[2] in [[1, 3], [3, 1]])
        assert_equal(pred[3], [0])
        assert_equal(dist, {0: 0, 1: 1, 2: 2, 3: 1}) 

def test_dijkstra_predecessor3(self):
        XG = nx.DiGraph()
        XG.add_weighted_edges_from([('s', 'u', 10), ('s', 'x', 5),
                                    ('u', 'v', 1), ('u', 'x', 2),
                                    ('v', 'y', 1), ('x', 'u', 3),
                                    ('x', 'v', 5), ('x', 'y', 2),
                                    ('y', 's', 7), ('y', 'v', 6)])
        (P, D) = nx.dijkstra_predecessor_and_distance(XG, 's')
        assert_equal(P['v'], ['u'])
        assert_equal(D['v'], 9)
        (P, D) = nx.dijkstra_predecessor_and_distance(XG, 's', cutoff=8)
        assert_false('v' in D) 

def test_dijkstra_pred_distance_multigraph(self):
        G = nx.MultiGraph()
        G.add_edge('a', 'b', key='short', foo=5, weight=100)
        G.add_edge('a', 'b', key='long', bar=1, weight=110)
        p, d = nx.dijkstra_predecessor_and_distance(G, 'a')
        assert_equal(p, {'a': [], 'b': ['a']})
        assert_equal(d, {'a': 0, 'b': 100}) 

def test_dijkstra_predecessor1(self):
        G = nx.path_graph(4)
        assert_equal(nx.dijkstra_predecessor_and_distance(G, 0),
                     ({0: [], 1: [0], 2: [1], 3: [2]}, {0: 0, 1: 1, 2: 2, 3: 3})) 

def test_dijkstra_predecessor2(self):
        # 4-cycle
        G = nx.Graph([(0,1),(1,2),(2,3),(3,0)])
        pred, dist = nx.dijkstra_predecessor_and_distance(G, (0))
        assert_equal(pred[0],[])
        assert_equal(pred[1],[0])
        assert_true(pred[2] in [[1,3],[3,1]])
        assert_equal(pred[3],[0])
        assert_equal(dist, {0: 0, 1: 1, 2: 2, 3: 1}) 

def test_dijkstra_predecessor3(self):
        XG = nx.DiGraph()
        XG.add_weighted_edges_from([('s', 'u', 10), ('s', 'x', 5),
                                    ('u', 'v', 1), ('u', 'x', 2),
                                    ('v', 'y', 1), ('x', 'u', 3),
                                    ('x', 'v', 5), ('x', 'y', 2),
                                    ('y', 's', 7), ('y', 'v', 6)])
        (P, D) = nx.dijkstra_predecessor_and_distance(XG, 's')
        assert_equal(P['v'], ['u'])
        assert_equal(D['v'], 9)
        (P, D) = nx.dijkstra_predecessor_and_distance(XG, 's', cutoff=8)
        assert_false('v' in D) 

def test_dijkstra_pred_distance_multigraph(self):
        G = nx.MultiGraph()
        G.add_edge('a', 'b', key='short', foo=5, weight=100)
        G.add_edge('a', 'b', key='long', bar=1, weight=110)
        p, d = nx.dijkstra_predecessor_and_distance(G, 'a')
        assert_equal(p, {'a': [], 'b': ['a']})
        assert_equal(d, {'a': 0, 'b': 100}) 

def test_negative_edge_cycle(self):
        G = nx.cycle_graph(5, create_using=nx.DiGraph())
        assert_equal(nx.negative_edge_cycle(G), False)
        G.add_edge(8, 9, weight=-7)
        G.add_edge(9, 8, weight=3)
        graph_size = len(G)
        assert_equal(nx.negative_edge_cycle(G), True)
        assert_equal(graph_size, len(G))
        assert_raises(ValueError, nx.single_source_dijkstra_path_length, G, 8)
        assert_raises(ValueError, nx.single_source_dijkstra, G, 8)
        assert_raises(ValueError, nx.dijkstra_predecessor_and_distance, G, 8)
        G.add_edge(9, 10)
        assert_raises(ValueError, nx.bidirectional_dijkstra, G, 8, 10) 

def _node_betweenness(G,source,cutoff=False,normalized=True,weight=None):
    """Node betweenness helper:
    see betweenness_centrality for what you probably want.

    This actually computes "load" and not betweenness.
    See https://networkx.lanl.gov/ticket/103

    This calculates the load of each node for paths from a single source.
    (The fraction of number of shortests paths from source that go
    through each node.)

    To get the load for a node you need to do all-pairs shortest paths.

    If weight is not None then use Dijkstra for finding shortest paths.
    In this case a cutoff is not implemented and so is ignored.

    """

    # get the predecessor and path length data
    if weight is None:
        (pred,length)=nx.predecessor(G,source,cutoff=cutoff,return_seen=True)
    else:
        (pred,length)=nx.dijkstra_predecessor_and_distance(G,source,weight=weight)

    # order the nodes by path length
    onodes = [ (l,vert) for (vert,l) in length.items() ]
    onodes.sort()
    onodes[:] = [vert for (l,vert) in onodes if l>0]

    # intialize betweenness
    between={}.fromkeys(length,1.0)

    while onodes:
        v=onodes.pop()
        if v in pred:
            num_paths=len(pred[v])   # Discount betweenness if more than
            for x in pred[v]:        # one shortest path.
                if x==source:   # stop if hit source because all remaining v
                    break       #  also have pred[v]==[source]
                between[x]+=between[v]/float(num_paths)
    #  remove source
    for v in between:
        between[v]-=1
    # rescale to be between 0 and 1
    if normalized:
        l=len(between)
        if l > 2:
            scale=1.0/float((l-1)*(l-2)) # 1/the number of possible paths
            for v in between:
                between[v] *= scale
    return between 

def _node_betweenness(G, source, cutoff=False, normalized=True,
                      weight=None):
    """Node betweenness_centrality helper:

    See betweenness_centrality for what you probably want.
    This actually computes "load" and not betweenness.
    See https://networkx.lanl.gov/ticket/103

    This calculates the load of each node for paths from a single source.
    (The fraction of number of shortests paths from source that go
    through each node.)

    To get the load for a node you need to do all-pairs shortest paths.

    If weight is not None then use Dijkstra for finding shortest paths.
    """
    # get the predecessor and path length data
    if weight is None:
        (pred, length) = nx.predecessor(G, source, cutoff=cutoff,
                                        return_seen=True)
    else:
        (pred, length) = nx.dijkstra_predecessor_and_distance(G, source,
                                                              cutoff, weight)

    # order the nodes by path length
    onodes = [(l, vert) for (vert, l) in length.items()]
    onodes.sort()
    onodes[:] = [vert for (l, vert) in onodes if l > 0]

    # initialize betweenness
    between = {}.fromkeys(length, 1.0)

    while onodes:
        v = onodes.pop()
        if v in pred:
            num_paths = len(pred[v])  # Discount betweenness if more than
            for x in pred[v]:         # one shortest path.
                if x == source:  # stop if hit source because all remaining v
                    break        # also have pred[v]==[source]
                between[x] += between[v] / float(num_paths)
    #  remove source
    for v in between:
        between[v] -= 1
    # rescale to be between 0 and 1
    if normalized:
        l = len(between)
        if l > 2:
            # scale by 1/the number of possible paths
            scale = 1.0 / float((l - 1) * (l - 2))
            for v in between:
                between[v] *= scale
    return between