aboutsummaryrefslogtreecommitdiff
path: root/.venv/lib/python3.12/site-packages/networkx/algorithms/flow/tests
diff options
context:
space:
mode:
Diffstat (limited to '.venv/lib/python3.12/site-packages/networkx/algorithms/flow/tests')
-rw-r--r--.venv/lib/python3.12/site-packages/networkx/algorithms/flow/tests/__init__.py0
-rw-r--r--.venv/lib/python3.12/site-packages/networkx/algorithms/flow/tests/gl1.gpickle.bz2bin0 -> 44623 bytes
-rw-r--r--.venv/lib/python3.12/site-packages/networkx/algorithms/flow/tests/gw1.gpickle.bz2bin0 -> 42248 bytes
-rw-r--r--.venv/lib/python3.12/site-packages/networkx/algorithms/flow/tests/netgen-2.gpickle.bz2bin0 -> 18972 bytes
-rw-r--r--.venv/lib/python3.12/site-packages/networkx/algorithms/flow/tests/test_gomory_hu.py128
-rw-r--r--.venv/lib/python3.12/site-packages/networkx/algorithms/flow/tests/test_maxflow.py573
-rw-r--r--.venv/lib/python3.12/site-packages/networkx/algorithms/flow/tests/test_maxflow_large_graph.py156
-rw-r--r--.venv/lib/python3.12/site-packages/networkx/algorithms/flow/tests/test_mincost.py476
-rw-r--r--.venv/lib/python3.12/site-packages/networkx/algorithms/flow/tests/test_networksimplex.py387
-rw-r--r--.venv/lib/python3.12/site-packages/networkx/algorithms/flow/tests/wlm3.gpickle.bz2bin0 -> 88132 bytes
10 files changed, 1720 insertions, 0 deletions
diff --git a/.venv/lib/python3.12/site-packages/networkx/algorithms/flow/tests/__init__.py b/.venv/lib/python3.12/site-packages/networkx/algorithms/flow/tests/__init__.py
new file mode 100644
index 00000000..e69de29b
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/networkx/algorithms/flow/tests/__init__.py
diff --git a/.venv/lib/python3.12/site-packages/networkx/algorithms/flow/tests/gl1.gpickle.bz2 b/.venv/lib/python3.12/site-packages/networkx/algorithms/flow/tests/gl1.gpickle.bz2
new file mode 100644
index 00000000..e6ed5744
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/networkx/algorithms/flow/tests/gl1.gpickle.bz2
Binary files differ
diff --git a/.venv/lib/python3.12/site-packages/networkx/algorithms/flow/tests/gw1.gpickle.bz2 b/.venv/lib/python3.12/site-packages/networkx/algorithms/flow/tests/gw1.gpickle.bz2
new file mode 100644
index 00000000..abd0e8a2
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/networkx/algorithms/flow/tests/gw1.gpickle.bz2
Binary files differ
diff --git a/.venv/lib/python3.12/site-packages/networkx/algorithms/flow/tests/netgen-2.gpickle.bz2 b/.venv/lib/python3.12/site-packages/networkx/algorithms/flow/tests/netgen-2.gpickle.bz2
new file mode 100644
index 00000000..cd3ea801
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/networkx/algorithms/flow/tests/netgen-2.gpickle.bz2
Binary files differ
diff --git a/.venv/lib/python3.12/site-packages/networkx/algorithms/flow/tests/test_gomory_hu.py b/.venv/lib/python3.12/site-packages/networkx/algorithms/flow/tests/test_gomory_hu.py
new file mode 100644
index 00000000..1649ec82
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/networkx/algorithms/flow/tests/test_gomory_hu.py
@@ -0,0 +1,128 @@
+from itertools import combinations
+
+import pytest
+
+import networkx as nx
+from networkx.algorithms.flow import (
+ boykov_kolmogorov,
+ dinitz,
+ edmonds_karp,
+ preflow_push,
+ shortest_augmenting_path,
+)
+
+flow_funcs = [
+ boykov_kolmogorov,
+ dinitz,
+ edmonds_karp,
+ preflow_push,
+ shortest_augmenting_path,
+]
+
+
+class TestGomoryHuTree:
+ def minimum_edge_weight(self, T, u, v):
+ path = nx.shortest_path(T, u, v, weight="weight")
+ return min((T[u][v]["weight"], (u, v)) for (u, v) in zip(path, path[1:]))
+
+ def compute_cutset(self, G, T_orig, edge):
+ T = T_orig.copy()
+ T.remove_edge(*edge)
+ U, V = list(nx.connected_components(T))
+ cutset = set()
+ for x, nbrs in ((n, G[n]) for n in U):
+ cutset.update((x, y) for y in nbrs if y in V)
+ return cutset
+
+ def test_default_flow_function_karate_club_graph(self):
+ G = nx.karate_club_graph()
+ nx.set_edge_attributes(G, 1, "capacity")
+ T = nx.gomory_hu_tree(G)
+ assert nx.is_tree(T)
+ for u, v in combinations(G, 2):
+ cut_value, edge = self.minimum_edge_weight(T, u, v)
+ assert nx.minimum_cut_value(G, u, v) == cut_value
+
+ def test_karate_club_graph(self):
+ G = nx.karate_club_graph()
+ nx.set_edge_attributes(G, 1, "capacity")
+ for flow_func in flow_funcs:
+ T = nx.gomory_hu_tree(G, flow_func=flow_func)
+ assert nx.is_tree(T)
+ for u, v in combinations(G, 2):
+ cut_value, edge = self.minimum_edge_weight(T, u, v)
+ assert nx.minimum_cut_value(G, u, v) == cut_value
+
+ def test_davis_southern_women_graph(self):
+ G = nx.davis_southern_women_graph()
+ nx.set_edge_attributes(G, 1, "capacity")
+ for flow_func in flow_funcs:
+ T = nx.gomory_hu_tree(G, flow_func=flow_func)
+ assert nx.is_tree(T)
+ for u, v in combinations(G, 2):
+ cut_value, edge = self.minimum_edge_weight(T, u, v)
+ assert nx.minimum_cut_value(G, u, v) == cut_value
+
+ def test_florentine_families_graph(self):
+ G = nx.florentine_families_graph()
+ nx.set_edge_attributes(G, 1, "capacity")
+ for flow_func in flow_funcs:
+ T = nx.gomory_hu_tree(G, flow_func=flow_func)
+ assert nx.is_tree(T)
+ for u, v in combinations(G, 2):
+ cut_value, edge = self.minimum_edge_weight(T, u, v)
+ assert nx.minimum_cut_value(G, u, v) == cut_value
+
+ @pytest.mark.slow
+ def test_les_miserables_graph_cutset(self):
+ G = nx.les_miserables_graph()
+ nx.set_edge_attributes(G, 1, "capacity")
+ for flow_func in flow_funcs:
+ T = nx.gomory_hu_tree(G, flow_func=flow_func)
+ assert nx.is_tree(T)
+ for u, v in combinations(G, 2):
+ cut_value, edge = self.minimum_edge_weight(T, u, v)
+ assert nx.minimum_cut_value(G, u, v) == cut_value
+
+ def test_karate_club_graph_cutset(self):
+ G = nx.karate_club_graph()
+ nx.set_edge_attributes(G, 1, "capacity")
+ T = nx.gomory_hu_tree(G)
+ assert nx.is_tree(T)
+ u, v = 0, 33
+ cut_value, edge = self.minimum_edge_weight(T, u, v)
+ cutset = self.compute_cutset(G, T, edge)
+ assert cut_value == len(cutset)
+
+ def test_wikipedia_example(self):
+ # Example from https://en.wikipedia.org/wiki/Gomory%E2%80%93Hu_tree
+ G = nx.Graph()
+ G.add_weighted_edges_from(
+ (
+ (0, 1, 1),
+ (0, 2, 7),
+ (1, 2, 1),
+ (1, 3, 3),
+ (1, 4, 2),
+ (2, 4, 4),
+ (3, 4, 1),
+ (3, 5, 6),
+ (4, 5, 2),
+ )
+ )
+ for flow_func in flow_funcs:
+ T = nx.gomory_hu_tree(G, capacity="weight", flow_func=flow_func)
+ assert nx.is_tree(T)
+ for u, v in combinations(G, 2):
+ cut_value, edge = self.minimum_edge_weight(T, u, v)
+ assert nx.minimum_cut_value(G, u, v, capacity="weight") == cut_value
+
+ def test_directed_raises(self):
+ with pytest.raises(nx.NetworkXNotImplemented):
+ G = nx.DiGraph()
+ T = nx.gomory_hu_tree(G)
+
+ def test_empty_raises(self):
+ with pytest.raises(nx.NetworkXError):
+ G = nx.empty_graph()
+ T = nx.gomory_hu_tree(G)
diff --git a/.venv/lib/python3.12/site-packages/networkx/algorithms/flow/tests/test_maxflow.py b/.venv/lib/python3.12/site-packages/networkx/algorithms/flow/tests/test_maxflow.py
new file mode 100644
index 00000000..d7305a7b
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/networkx/algorithms/flow/tests/test_maxflow.py
@@ -0,0 +1,573 @@
+"""Maximum flow algorithms test suite."""
+
+import pytest
+
+import networkx as nx
+from networkx.algorithms.flow import (
+ boykov_kolmogorov,
+ build_flow_dict,
+ build_residual_network,
+ dinitz,
+ edmonds_karp,
+ preflow_push,
+ shortest_augmenting_path,
+)
+
+flow_funcs = {
+ boykov_kolmogorov,
+ dinitz,
+ edmonds_karp,
+ preflow_push,
+ shortest_augmenting_path,
+}
+
+max_min_funcs = {nx.maximum_flow, nx.minimum_cut}
+flow_value_funcs = {nx.maximum_flow_value, nx.minimum_cut_value}
+interface_funcs = max_min_funcs | flow_value_funcs
+all_funcs = flow_funcs | interface_funcs
+
+
+def compute_cutset(G, partition):
+ reachable, non_reachable = partition
+ cutset = set()
+ for u, nbrs in ((n, G[n]) for n in reachable):
+ cutset.update((u, v) for v in nbrs if v in non_reachable)
+ return cutset
+
+
+def validate_flows(G, s, t, flowDict, solnValue, capacity, flow_func):
+ errmsg = f"Assertion failed in function: {flow_func.__name__}"
+ assert set(G) == set(flowDict), errmsg
+ for u in G:
+ assert set(G[u]) == set(flowDict[u]), errmsg
+ excess = {u: 0 for u in flowDict}
+ for u in flowDict:
+ for v, flow in flowDict[u].items():
+ if capacity in G[u][v]:
+ assert flow <= G[u][v][capacity]
+ assert flow >= 0, errmsg
+ excess[u] -= flow
+ excess[v] += flow
+ for u, exc in excess.items():
+ if u == s:
+ assert exc == -solnValue, errmsg
+ elif u == t:
+ assert exc == solnValue, errmsg
+ else:
+ assert exc == 0, errmsg
+
+
+def validate_cuts(G, s, t, solnValue, partition, capacity, flow_func):
+ errmsg = f"Assertion failed in function: {flow_func.__name__}"
+ assert all(n in G for n in partition[0]), errmsg
+ assert all(n in G for n in partition[1]), errmsg
+ cutset = compute_cutset(G, partition)
+ assert all(G.has_edge(u, v) for (u, v) in cutset), errmsg
+ assert solnValue == sum(G[u][v][capacity] for (u, v) in cutset), errmsg
+ H = G.copy()
+ H.remove_edges_from(cutset)
+ if not G.is_directed():
+ assert not nx.is_connected(H), errmsg
+ else:
+ assert not nx.is_strongly_connected(H), errmsg
+
+
+def compare_flows_and_cuts(G, s, t, solnValue, capacity="capacity"):
+ for flow_func in flow_funcs:
+ errmsg = f"Assertion failed in function: {flow_func.__name__}"
+ R = flow_func(G, s, t, capacity)
+ # Test both legacy and new implementations.
+ flow_value = R.graph["flow_value"]
+ flow_dict = build_flow_dict(G, R)
+ assert flow_value == solnValue, errmsg
+ validate_flows(G, s, t, flow_dict, solnValue, capacity, flow_func)
+ # Minimum cut
+ cut_value, partition = nx.minimum_cut(
+ G, s, t, capacity=capacity, flow_func=flow_func
+ )
+ validate_cuts(G, s, t, solnValue, partition, capacity, flow_func)
+
+
+class TestMaxflowMinCutCommon:
+ def test_graph1(self):
+ # Trivial undirected graph
+ G = nx.Graph()
+ G.add_edge(1, 2, capacity=1.0)
+
+ # solution flows
+ # {1: {2: 1.0}, 2: {1: 1.0}}
+
+ compare_flows_and_cuts(G, 1, 2, 1.0)
+
+ def test_graph2(self):
+ # A more complex undirected graph
+ # adapted from https://web.archive.org/web/20220815055650/https://www.topcoder.com/thrive/articles/Maximum%20Flow:%20Part%20One
+ G = nx.Graph()
+ 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)
+
+ # H
+ # {
+ # "x": {"a": 3, "b": 1},
+ # "a": {"c": 3, "x": 3},
+ # "b": {"c": 1, "d": 2, "x": 1},
+ # "c": {"a": 3, "b": 1, "y": 2},
+ # "d": {"b": 2, "e": 2},
+ # "e": {"d": 2, "y": 2},
+ # "y": {"c": 2, "e": 2},
+ # }
+
+ compare_flows_and_cuts(G, "x", "y", 4.0)
+
+ def test_digraph1(self):
+ # The classic directed graph example
+ G = nx.DiGraph()
+ G.add_edge("a", "b", capacity=1000.0)
+ G.add_edge("a", "c", capacity=1000.0)
+ G.add_edge("b", "c", capacity=1.0)
+ G.add_edge("b", "d", capacity=1000.0)
+ G.add_edge("c", "d", capacity=1000.0)
+
+ # H
+ # {
+ # "a": {"b": 1000.0, "c": 1000.0},
+ # "b": {"c": 0, "d": 1000.0},
+ # "c": {"d": 1000.0},
+ # "d": {},
+ # }
+
+ compare_flows_and_cuts(G, "a", "d", 2000.0)
+
+ def test_digraph2(self):
+ # An example in which some edges end up with zero flow.
+ G = nx.DiGraph()
+ G.add_edge("s", "b", capacity=2)
+ G.add_edge("s", "c", capacity=1)
+ G.add_edge("c", "d", capacity=1)
+ G.add_edge("d", "a", capacity=1)
+ G.add_edge("b", "a", capacity=2)
+ G.add_edge("a", "t", capacity=2)
+
+ # H
+ # {
+ # "s": {"b": 2, "c": 0},
+ # "c": {"d": 0},
+ # "d": {"a": 0},
+ # "b": {"a": 2},
+ # "a": {"t": 2},
+ # "t": {},
+ # }
+
+ compare_flows_and_cuts(G, "s", "t", 2)
+
+ def test_digraph3(self):
+ # A directed graph example from Cormen et al.
+ G = nx.DiGraph()
+ G.add_edge("s", "v1", capacity=16.0)
+ G.add_edge("s", "v2", capacity=13.0)
+ G.add_edge("v1", "v2", capacity=10.0)
+ G.add_edge("v2", "v1", capacity=4.0)
+ G.add_edge("v1", "v3", capacity=12.0)
+ G.add_edge("v3", "v2", capacity=9.0)
+ G.add_edge("v2", "v4", capacity=14.0)
+ G.add_edge("v4", "v3", capacity=7.0)
+ G.add_edge("v3", "t", capacity=20.0)
+ G.add_edge("v4", "t", capacity=4.0)
+
+ # H
+ # {
+ # "s": {"v1": 12.0, "v2": 11.0},
+ # "v2": {"v1": 0, "v4": 11.0},
+ # "v1": {"v2": 0, "v3": 12.0},
+ # "v3": {"v2": 0, "t": 19.0},
+ # "v4": {"v3": 7.0, "t": 4.0},
+ # "t": {},
+ # }
+
+ compare_flows_and_cuts(G, "s", "t", 23.0)
+
+ def test_digraph4(self):
+ # A more complex directed graph
+ # from https://web.archive.org/web/20220815055650/https://www.topcoder.com/thrive/articles/Maximum%20Flow:%20Part%20One
+ 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)
+
+ # H
+ # {
+ # "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": {},
+ # }
+
+ compare_flows_and_cuts(G, "x", "y", 3.0)
+
+ def test_wikipedia_dinitz_example(self):
+ # Nice example from https://en.wikipedia.org/wiki/Dinic's_algorithm
+ G = nx.DiGraph()
+ G.add_edge("s", 1, capacity=10)
+ G.add_edge("s", 2, capacity=10)
+ G.add_edge(1, 3, capacity=4)
+ G.add_edge(1, 4, capacity=8)
+ G.add_edge(1, 2, capacity=2)
+ G.add_edge(2, 4, capacity=9)
+ G.add_edge(3, "t", capacity=10)
+ G.add_edge(4, 3, capacity=6)
+ G.add_edge(4, "t", capacity=10)
+
+ # solution flows
+ # {
+ # 1: {2: 0, 3: 4, 4: 6},
+ # 2: {4: 9},
+ # 3: {"t": 9},
+ # 4: {3: 5, "t": 10},
+ # "s": {1: 10, 2: 9},
+ # "t": {},
+ # }
+
+ compare_flows_and_cuts(G, "s", "t", 19)
+
+ 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)
+
+ # solution flows
+ # {
+ # "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"
+
+ compare_flows_and_cuts(G, s, t, solnValue, capacity="spam")
+
+ def test_digraph_infcap_edges(self):
+ # DiGraph with infinite capacity edges
+ G = nx.DiGraph()
+ G.add_edge("s", "a")
+ G.add_edge("s", "b", capacity=30)
+ G.add_edge("a", "c", capacity=25)
+ G.add_edge("b", "c", capacity=12)
+ G.add_edge("a", "t", capacity=60)
+ G.add_edge("c", "t")
+
+ # H
+ # {
+ # "s": {"a": 85, "b": 12},
+ # "a": {"c": 25, "t": 60},
+ # "b": {"c": 12},
+ # "c": {"t": 37},
+ # "t": {},
+ # }
+
+ compare_flows_and_cuts(G, "s", "t", 97)
+
+ # DiGraph with infinite capacity digon
+ G = nx.DiGraph()
+ G.add_edge("s", "a", capacity=85)
+ G.add_edge("s", "b", capacity=30)
+ G.add_edge("a", "c")
+ G.add_edge("c", "a")
+ G.add_edge("b", "c", capacity=12)
+ G.add_edge("a", "t", capacity=60)
+ G.add_edge("c", "t", capacity=37)
+
+ # H
+ # {
+ # "s": {"a": 85, "b": 12},
+ # "a": {"c": 25, "t": 60},
+ # "c": {"a": 0, "t": 37},
+ # "b": {"c": 12},
+ # "t": {},
+ # }
+
+ compare_flows_and_cuts(G, "s", "t", 97)
+
+ 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")
+
+ for flow_func in all_funcs:
+ pytest.raises(nx.NetworkXUnbounded, flow_func, G, "s", "t")
+
+ def test_graph_infcap_edges(self):
+ # Undirected graph with infinite capacity edges
+ G = nx.Graph()
+ G.add_edge("s", "a")
+ G.add_edge("s", "b", capacity=30)
+ G.add_edge("a", "c", capacity=25)
+ G.add_edge("b", "c", capacity=12)
+ G.add_edge("a", "t", capacity=60)
+ G.add_edge("c", "t")
+
+ # H
+ # {
+ # "s": {"a": 85, "b": 12},
+ # "a": {"c": 25, "s": 85, "t": 60},
+ # "b": {"c": 12, "s": 12},
+ # "c": {"a": 25, "b": 12, "t": 37},
+ # "t": {"a": 60, "c": 37},
+ # }
+
+ compare_flows_and_cuts(G, "s", "t", 97)
+
+ def test_digraph5(self):
+ # From ticket #429 by mfrasca.
+ G = nx.DiGraph()
+ G.add_edge("s", "a", capacity=2)
+ G.add_edge("s", "b", capacity=2)
+ G.add_edge("a", "b", capacity=5)
+ G.add_edge("a", "t", capacity=1)
+ G.add_edge("b", "a", capacity=1)
+ G.add_edge("b", "t", capacity=3)
+ # flow solution
+ # {
+ # "a": {"b": 1, "t": 1},
+ # "b": {"a": 0, "t": 3},
+ # "s": {"a": 2, "b": 2},
+ # "t": {},
+ # }
+ compare_flows_and_cuts(G, "s", "t", 4)
+
+ 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
+ # flow solution
+ # {0: {}, 2: {3: 0}, 3: {2: 0}}
+ compare_flows_and_cuts(G, 0, 3, 0)
+
+ def test_source_target_not_in_graph(self):
+ G = nx.Graph()
+ G.add_weighted_edges_from([(0, 1, 1), (1, 2, 1), (2, 3, 1)], weight="capacity")
+ G.remove_node(0)
+ for flow_func in all_funcs:
+ pytest.raises(nx.NetworkXError, flow_func, G, 0, 3)
+ G.add_weighted_edges_from([(0, 1, 1), (1, 2, 1), (2, 3, 1)], weight="capacity")
+ G.remove_node(3)
+ for flow_func in all_funcs:
+ pytest.raises(nx.NetworkXError, flow_func, G, 0, 3)
+
+ def test_source_target_coincide(self):
+ G = nx.Graph()
+ G.add_node(0)
+ for flow_func in all_funcs:
+ pytest.raises(nx.NetworkXError, flow_func, G, 0, 0)
+
+ def test_multigraphs_raise(self):
+ G = nx.MultiGraph()
+ M = nx.MultiDiGraph()
+ G.add_edges_from([(0, 1), (1, 0)], capacity=True)
+ for flow_func in all_funcs:
+ pytest.raises(nx.NetworkXError, flow_func, G, 0, 0)
+
+
+class TestMaxFlowMinCutInterface:
+ def setup_method(self):
+ 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)
+ self.G = G
+ H = nx.DiGraph()
+ H.add_edge(0, 1, capacity=1.0)
+ H.add_edge(1, 2, capacity=1.0)
+ self.H = H
+
+ def test_flow_func_not_callable(self):
+ elements = ["this_should_be_callable", 10, {1, 2, 3}]
+ G = nx.Graph()
+ G.add_weighted_edges_from([(0, 1, 1), (1, 2, 1), (2, 3, 1)], weight="capacity")
+ for flow_func in interface_funcs:
+ for element in elements:
+ pytest.raises(nx.NetworkXError, flow_func, G, 0, 1, flow_func=element)
+ pytest.raises(nx.NetworkXError, flow_func, G, 0, 1, flow_func=element)
+
+ def test_flow_func_parameters(self):
+ G = self.G
+ fv = 3.0
+ for interface_func in interface_funcs:
+ for flow_func in flow_funcs:
+ errmsg = (
+ f"Assertion failed in function: {flow_func.__name__} "
+ f"in interface {interface_func.__name__}"
+ )
+ result = interface_func(G, "x", "y", flow_func=flow_func)
+ if interface_func in max_min_funcs:
+ result = result[0]
+ assert fv == result, errmsg
+
+ def test_minimum_cut_no_cutoff(self):
+ G = self.G
+ pytest.raises(
+ nx.NetworkXError,
+ nx.minimum_cut,
+ G,
+ "x",
+ "y",
+ flow_func=preflow_push,
+ cutoff=1.0,
+ )
+ pytest.raises(
+ nx.NetworkXError,
+ nx.minimum_cut_value,
+ G,
+ "x",
+ "y",
+ flow_func=preflow_push,
+ cutoff=1.0,
+ )
+
+ def test_kwargs(self):
+ G = self.H
+ fv = 1.0
+ to_test = (
+ (shortest_augmenting_path, {"two_phase": True}),
+ (preflow_push, {"global_relabel_freq": 5}),
+ )
+ for interface_func in interface_funcs:
+ for flow_func, kwargs in to_test:
+ errmsg = (
+ f"Assertion failed in function: {flow_func.__name__} "
+ f"in interface {interface_func.__name__}"
+ )
+ result = interface_func(G, 0, 2, flow_func=flow_func, **kwargs)
+ if interface_func in max_min_funcs:
+ result = result[0]
+ assert fv == result, errmsg
+
+ def test_kwargs_default_flow_func(self):
+ G = self.H
+ for interface_func in interface_funcs:
+ pytest.raises(
+ nx.NetworkXError, interface_func, G, 0, 1, global_relabel_freq=2
+ )
+
+ def test_reusing_residual(self):
+ G = self.G
+ fv = 3.0
+ s, t = "x", "y"
+ R = build_residual_network(G, "capacity")
+ for interface_func in interface_funcs:
+ for flow_func in flow_funcs:
+ errmsg = (
+ f"Assertion failed in function: {flow_func.__name__} "
+ f"in interface {interface_func.__name__}"
+ )
+ for i in range(3):
+ result = interface_func(
+ G, "x", "y", flow_func=flow_func, residual=R
+ )
+ if interface_func in max_min_funcs:
+ result = result[0]
+ assert fv == result, errmsg
+
+
+# Tests specific to one algorithm
+def test_preflow_push_global_relabel_freq():
+ G = nx.DiGraph()
+ G.add_edge(1, 2, capacity=1)
+ R = preflow_push(G, 1, 2, global_relabel_freq=None)
+ assert R.graph["flow_value"] == 1
+ pytest.raises(nx.NetworkXError, preflow_push, G, 1, 2, global_relabel_freq=-1)
+
+
+def test_preflow_push_makes_enough_space():
+ # From ticket #1542
+ G = nx.DiGraph()
+ nx.add_path(G, [0, 1, 3], capacity=1)
+ nx.add_path(G, [1, 2, 3], capacity=1)
+ R = preflow_push(G, 0, 3, value_only=False)
+ assert R.graph["flow_value"] == 1
+
+
+def test_shortest_augmenting_path_two_phase():
+ k = 5
+ p = 1000
+ G = nx.DiGraph()
+ for i in range(k):
+ G.add_edge("s", (i, 0), capacity=1)
+ nx.add_path(G, ((i, j) for j in range(p)), capacity=1)
+ G.add_edge((i, p - 1), "t", capacity=1)
+ R = shortest_augmenting_path(G, "s", "t", two_phase=True)
+ assert R.graph["flow_value"] == k
+ R = shortest_augmenting_path(G, "s", "t", two_phase=False)
+ assert R.graph["flow_value"] == k
+
+
+class TestCutoff:
+ def test_cutoff(self):
+ k = 5
+ p = 1000
+ G = nx.DiGraph()
+ for i in range(k):
+ G.add_edge("s", (i, 0), capacity=2)
+ nx.add_path(G, ((i, j) for j in range(p)), capacity=2)
+ G.add_edge((i, p - 1), "t", capacity=2)
+ R = shortest_augmenting_path(G, "s", "t", two_phase=True, cutoff=k)
+ assert k <= R.graph["flow_value"] <= (2 * k)
+ R = shortest_augmenting_path(G, "s", "t", two_phase=False, cutoff=k)
+ assert k <= R.graph["flow_value"] <= (2 * k)
+ R = edmonds_karp(G, "s", "t", cutoff=k)
+ assert k <= R.graph["flow_value"] <= (2 * k)
+ R = dinitz(G, "s", "t", cutoff=k)
+ assert k <= R.graph["flow_value"] <= (2 * k)
+ R = boykov_kolmogorov(G, "s", "t", cutoff=k)
+ assert k <= R.graph["flow_value"] <= (2 * k)
+
+ 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,
+ dinitz,
+ boykov_kolmogorov,
+ ]:
+ for cutoff in [3, 2, 1]:
+ result = nx.maximum_flow_value(
+ G, 0, 4, flow_func=flow_func, cutoff=cutoff
+ )
+ assert cutoff == result, f"cutoff error in {flow_func.__name__}"
diff --git a/.venv/lib/python3.12/site-packages/networkx/algorithms/flow/tests/test_maxflow_large_graph.py b/.venv/lib/python3.12/site-packages/networkx/algorithms/flow/tests/test_maxflow_large_graph.py
new file mode 100644
index 00000000..b395cbc8
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/networkx/algorithms/flow/tests/test_maxflow_large_graph.py
@@ -0,0 +1,156 @@
+"""Maximum flow algorithms test suite on large graphs."""
+
+import bz2
+import importlib.resources
+import os
+import pickle
+
+import pytest
+
+import networkx as nx
+from networkx.algorithms.flow import (
+ boykov_kolmogorov,
+ build_flow_dict,
+ build_residual_network,
+ dinitz,
+ edmonds_karp,
+ preflow_push,
+ shortest_augmenting_path,
+)
+
+flow_funcs = [
+ boykov_kolmogorov,
+ dinitz,
+ edmonds_karp,
+ preflow_push,
+ shortest_augmenting_path,
+]
+
+
+def gen_pyramid(N):
+ # This graph admits a flow of value 1 for which every arc is at
+ # capacity (except the arcs incident to the sink which have
+ # infinite capacity).
+ G = nx.DiGraph()
+
+ for i in range(N - 1):
+ cap = 1.0 / (i + 2)
+ for j in range(i + 1):
+ G.add_edge((i, j), (i + 1, j), capacity=cap)
+ cap = 1.0 / (i + 1) - cap
+ G.add_edge((i, j), (i + 1, j + 1), capacity=cap)
+ cap = 1.0 / (i + 2) - cap
+
+ for j in range(N):
+ G.add_edge((N - 1, j), "t")
+
+ return G
+
+
+def read_graph(name):
+ fname = (
+ importlib.resources.files("networkx.algorithms.flow.tests")
+ / f"{name}.gpickle.bz2"
+ )
+
+ with bz2.BZ2File(fname, "rb") as f:
+ G = pickle.load(f)
+ return G
+
+
+def validate_flows(G, s, t, soln_value, R, flow_func):
+ flow_value = R.graph["flow_value"]
+ flow_dict = build_flow_dict(G, R)
+ errmsg = f"Assertion failed in function: {flow_func.__name__}"
+ assert soln_value == flow_value, errmsg
+ assert set(G) == set(flow_dict), errmsg
+ for u in G:
+ assert set(G[u]) == set(flow_dict[u]), errmsg
+ excess = {u: 0 for u in flow_dict}
+ for u in flow_dict:
+ for v, flow in flow_dict[u].items():
+ assert flow <= G[u][v].get("capacity", float("inf")), errmsg
+ assert flow >= 0, errmsg
+ excess[u] -= flow
+ excess[v] += flow
+ for u, exc in excess.items():
+ if u == s:
+ assert exc == -soln_value, errmsg
+ elif u == t:
+ assert exc == soln_value, errmsg
+ else:
+ assert exc == 0, errmsg
+
+
+class TestMaxflowLargeGraph:
+ 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 = {"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 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 = {"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 flow_value == pytest.approx(1.0, abs=1e-7)
+
+ def test_gl1(self):
+ G = read_graph("gl1")
+ s = 1
+ t = len(G)
+ R = build_residual_network(G, "capacity")
+ kwargs = {"residual": R}
+
+ # do one flow_func to save time
+ flow_func = flow_funcs[0]
+ validate_flows(G, s, t, 156545, flow_func(G, s, t, **kwargs), flow_func)
+
+ # for flow_func in flow_funcs:
+ # validate_flows(G, s, t, 156545, flow_func(G, s, t, **kwargs),
+ # flow_func)
+
+ @pytest.mark.slow
+ def test_gw1(self):
+ G = read_graph("gw1")
+ s = 1
+ t = len(G)
+ R = build_residual_network(G, "capacity")
+ kwargs = {"residual": R}
+
+ for flow_func in flow_funcs:
+ validate_flows(G, s, t, 1202018, flow_func(G, s, t, **kwargs), flow_func)
+
+ def test_wlm3(self):
+ G = read_graph("wlm3")
+ s = 1
+ t = len(G)
+ R = build_residual_network(G, "capacity")
+ kwargs = {"residual": R}
+
+ # do one flow_func to save time
+ flow_func = flow_funcs[0]
+ validate_flows(G, s, t, 11875108, flow_func(G, s, t, **kwargs), flow_func)
+
+ # for flow_func in flow_funcs:
+ # validate_flows(G, s, t, 11875108, flow_func(G, s, t, **kwargs),
+ # flow_func)
+
+ def test_preflow_push_global_relabel(self):
+ G = read_graph("gw1")
+ R = preflow_push(G, 1, len(G), global_relabel_freq=50)
+ assert R.graph["flow_value"] == 1202018
diff --git a/.venv/lib/python3.12/site-packages/networkx/algorithms/flow/tests/test_mincost.py b/.venv/lib/python3.12/site-packages/networkx/algorithms/flow/tests/test_mincost.py
new file mode 100644
index 00000000..5b1794b1
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/networkx/algorithms/flow/tests/test_mincost.py
@@ -0,0 +1,476 @@
+import bz2
+import importlib.resources
+import os
+import pickle
+
+import pytest
+
+import networkx as nx
+
+
+class TestMinCostFlow:
+ def test_simple_digraph(self):
+ G = nx.DiGraph()
+ G.add_node("a", demand=-5)
+ G.add_node("d", demand=5)
+ G.add_edge("a", "b", weight=3, capacity=4)
+ G.add_edge("a", "c", weight=6, capacity=10)
+ G.add_edge("b", "d", weight=1, capacity=9)
+ G.add_edge("c", "d", weight=2, capacity=5)
+ flowCost, H = nx.network_simplex(G)
+ soln = {"a": {"b": 4, "c": 1}, "b": {"d": 4}, "c": {"d": 1}, "d": {}}
+ assert flowCost == 24
+ assert nx.min_cost_flow_cost(G) == 24
+ assert H == soln
+ assert nx.min_cost_flow(G) == soln
+ assert nx.cost_of_flow(G, H) == 24
+
+ flowCost, H = nx.capacity_scaling(G)
+ assert flowCost == 24
+ assert nx.cost_of_flow(G, H) == 24
+ assert H == soln
+
+ def test_negcycle_infcap(self):
+ G = nx.DiGraph()
+ G.add_node("s", demand=-5)
+ G.add_node("t", demand=5)
+ G.add_edge("s", "a", weight=1, capacity=3)
+ G.add_edge("a", "b", weight=3)
+ G.add_edge("c", "a", weight=-6)
+ G.add_edge("b", "d", weight=1)
+ G.add_edge("d", "c", weight=-2)
+ G.add_edge("d", "t", weight=1, capacity=3)
+ pytest.raises(nx.NetworkXUnfeasible, nx.network_simplex, G)
+ pytest.raises(nx.NetworkXUnbounded, nx.capacity_scaling, G)
+
+ def test_sum_demands_not_zero(self):
+ G = nx.DiGraph()
+ G.add_node("s", demand=-5)
+ G.add_node("t", demand=4)
+ G.add_edge("s", "a", weight=1, capacity=3)
+ G.add_edge("a", "b", weight=3)
+ G.add_edge("a", "c", weight=-6)
+ G.add_edge("b", "d", weight=1)
+ G.add_edge("c", "d", weight=-2)
+ G.add_edge("d", "t", weight=1, capacity=3)
+ pytest.raises(nx.NetworkXUnfeasible, nx.network_simplex, G)
+ pytest.raises(nx.NetworkXUnfeasible, nx.capacity_scaling, G)
+
+ def test_no_flow_satisfying_demands(self):
+ G = nx.DiGraph()
+ G.add_node("s", demand=-5)
+ G.add_node("t", demand=5)
+ G.add_edge("s", "a", weight=1, capacity=3)
+ G.add_edge("a", "b", weight=3)
+ G.add_edge("a", "c", weight=-6)
+ G.add_edge("b", "d", weight=1)
+ G.add_edge("c", "d", weight=-2)
+ G.add_edge("d", "t", weight=1, capacity=3)
+ pytest.raises(nx.NetworkXUnfeasible, nx.network_simplex, G)
+ pytest.raises(nx.NetworkXUnfeasible, nx.capacity_scaling, G)
+
+ def test_transshipment(self):
+ G = nx.DiGraph()
+ G.add_node("a", demand=1)
+ G.add_node("b", demand=-2)
+ G.add_node("c", demand=-2)
+ G.add_node("d", demand=3)
+ G.add_node("e", demand=-4)
+ G.add_node("f", demand=-4)
+ G.add_node("g", demand=3)
+ G.add_node("h", demand=2)
+ G.add_node("r", demand=3)
+ G.add_edge("a", "c", weight=3)
+ G.add_edge("r", "a", weight=2)
+ G.add_edge("b", "a", weight=9)
+ G.add_edge("r", "c", weight=0)
+ G.add_edge("b", "r", weight=-6)
+ G.add_edge("c", "d", weight=5)
+ G.add_edge("e", "r", weight=4)
+ G.add_edge("e", "f", weight=3)
+ G.add_edge("h", "b", weight=4)
+ G.add_edge("f", "d", weight=7)
+ G.add_edge("f", "h", weight=12)
+ G.add_edge("g", "d", weight=12)
+ G.add_edge("f", "g", weight=-1)
+ G.add_edge("h", "g", weight=-10)
+ flowCost, H = nx.network_simplex(G)
+ soln = {
+ "a": {"c": 0},
+ "b": {"a": 0, "r": 2},
+ "c": {"d": 3},
+ "d": {},
+ "e": {"r": 3, "f": 1},
+ "f": {"d": 0, "g": 3, "h": 2},
+ "g": {"d": 0},
+ "h": {"b": 0, "g": 0},
+ "r": {"a": 1, "c": 1},
+ }
+ assert flowCost == 41
+ assert nx.min_cost_flow_cost(G) == 41
+ assert H == soln
+ assert nx.min_cost_flow(G) == soln
+ assert nx.cost_of_flow(G, H) == 41
+
+ flowCost, H = nx.capacity_scaling(G)
+ assert flowCost == 41
+ assert nx.cost_of_flow(G, H) == 41
+ assert H == soln
+
+ def test_max_flow_min_cost(self):
+ G = nx.DiGraph()
+ G.add_edge("s", "a", bandwidth=6)
+ G.add_edge("s", "c", bandwidth=10, cost=10)
+ G.add_edge("a", "b", cost=6)
+ G.add_edge("b", "d", bandwidth=8, cost=7)
+ G.add_edge("c", "d", cost=10)
+ G.add_edge("d", "t", bandwidth=5, cost=5)
+ soln = {
+ "s": {"a": 5, "c": 0},
+ "a": {"b": 5},
+ "b": {"d": 5},
+ "c": {"d": 0},
+ "d": {"t": 5},
+ "t": {},
+ }
+ flow = nx.max_flow_min_cost(G, "s", "t", capacity="bandwidth", weight="cost")
+ assert flow == soln
+ assert nx.cost_of_flow(G, flow, weight="cost") == 90
+
+ G.add_edge("t", "s", cost=-100)
+ flowCost, flow = nx.capacity_scaling(G, capacity="bandwidth", weight="cost")
+ G.remove_edge("t", "s")
+ assert flowCost == -410
+ assert flow["t"]["s"] == 5
+ del flow["t"]["s"]
+ assert flow == soln
+ assert nx.cost_of_flow(G, flow, weight="cost") == 90
+
+ def test_digraph1(self):
+ # From Bradley, S. P., Hax, A. C. and Magnanti, T. L. Applied
+ # Mathematical Programming. Addison-Wesley, 1977.
+ G = nx.DiGraph()
+ G.add_node(1, demand=-20)
+ G.add_node(4, demand=5)
+ G.add_node(5, demand=15)
+ G.add_edges_from(
+ [
+ (1, 2, {"capacity": 15, "weight": 4}),
+ (1, 3, {"capacity": 8, "weight": 4}),
+ (2, 3, {"weight": 2}),
+ (2, 4, {"capacity": 4, "weight": 2}),
+ (2, 5, {"capacity": 10, "weight": 6}),
+ (3, 4, {"capacity": 15, "weight": 1}),
+ (3, 5, {"capacity": 5, "weight": 3}),
+ (4, 5, {"weight": 2}),
+ (5, 3, {"capacity": 4, "weight": 1}),
+ ]
+ )
+ flowCost, H = nx.network_simplex(G)
+ soln = {
+ 1: {2: 12, 3: 8},
+ 2: {3: 8, 4: 4, 5: 0},
+ 3: {4: 11, 5: 5},
+ 4: {5: 10},
+ 5: {3: 0},
+ }
+ assert flowCost == 150
+ assert nx.min_cost_flow_cost(G) == 150
+ assert H == soln
+ assert nx.min_cost_flow(G) == soln
+ assert nx.cost_of_flow(G, H) == 150
+
+ flowCost, H = nx.capacity_scaling(G)
+ assert flowCost == 150
+ assert H == soln
+ assert nx.cost_of_flow(G, H) == 150
+
+ def test_digraph2(self):
+ # Example from ticket #430 from mfrasca. Original source:
+ # http://www.cs.princeton.edu/courses/archive/spr03/cs226/lectures/mincost.4up.pdf, slide 11.
+ G = nx.DiGraph()
+ G.add_edge("s", 1, capacity=12)
+ G.add_edge("s", 2, capacity=6)
+ G.add_edge("s", 3, capacity=14)
+ G.add_edge(1, 2, capacity=11, weight=4)
+ G.add_edge(2, 3, capacity=9, weight=6)
+ G.add_edge(1, 4, capacity=5, weight=5)
+ G.add_edge(1, 5, capacity=2, weight=12)
+ G.add_edge(2, 5, capacity=4, weight=4)
+ G.add_edge(2, 6, capacity=2, weight=6)
+ G.add_edge(3, 6, capacity=31, weight=3)
+ G.add_edge(4, 5, capacity=18, weight=4)
+ G.add_edge(5, 6, capacity=9, weight=5)
+ G.add_edge(4, "t", capacity=3)
+ G.add_edge(5, "t", capacity=7)
+ G.add_edge(6, "t", capacity=22)
+ flow = nx.max_flow_min_cost(G, "s", "t")
+ soln = {
+ 1: {2: 6, 4: 5, 5: 1},
+ 2: {3: 6, 5: 4, 6: 2},
+ 3: {6: 20},
+ 4: {5: 2, "t": 3},
+ 5: {6: 0, "t": 7},
+ 6: {"t": 22},
+ "s": {1: 12, 2: 6, 3: 14},
+ "t": {},
+ }
+ assert flow == soln
+
+ G.add_edge("t", "s", weight=-100)
+ flowCost, flow = nx.capacity_scaling(G)
+ G.remove_edge("t", "s")
+ assert flow["t"]["s"] == 32
+ assert flowCost == -3007
+ del flow["t"]["s"]
+ assert flow == soln
+ assert nx.cost_of_flow(G, flow) == 193
+
+ def test_digraph3(self):
+ """Combinatorial Optimization: Algorithms and Complexity,
+ Papadimitriou Steiglitz at page 140 has an example, 7.1, but that
+ admits multiple solutions, so I alter it a bit. From ticket #430
+ by mfrasca."""
+
+ G = nx.DiGraph()
+ G.add_edge("s", "a")
+ G["s"]["a"].update({0: 2, 1: 4})
+ G.add_edge("s", "b")
+ G["s"]["b"].update({0: 2, 1: 1})
+ G.add_edge("a", "b")
+ G["a"]["b"].update({0: 5, 1: 2})
+ G.add_edge("a", "t")
+ G["a"]["t"].update({0: 1, 1: 5})
+ G.add_edge("b", "a")
+ G["b"]["a"].update({0: 1, 1: 3})
+ G.add_edge("b", "t")
+ G["b"]["t"].update({0: 3, 1: 2})
+
+ "PS.ex.7.1: testing main function"
+ sol = nx.max_flow_min_cost(G, "s", "t", capacity=0, weight=1)
+ flow = sum(v for v in sol["s"].values())
+ assert 4 == flow
+ assert 23 == nx.cost_of_flow(G, sol, weight=1)
+ assert sol["s"] == {"a": 2, "b": 2}
+ assert sol["a"] == {"b": 1, "t": 1}
+ assert sol["b"] == {"a": 0, "t": 3}
+ assert sol["t"] == {}
+
+ G.add_edge("t", "s")
+ G["t"]["s"].update({1: -100})
+ flowCost, sol = nx.capacity_scaling(G, capacity=0, weight=1)
+ G.remove_edge("t", "s")
+ flow = sum(v for v in sol["s"].values())
+ assert 4 == flow
+ assert sol["t"]["s"] == 4
+ assert flowCost == -377
+ del sol["t"]["s"]
+ assert sol["s"] == {"a": 2, "b": 2}
+ assert sol["a"] == {"b": 1, "t": 1}
+ assert sol["b"] == {"a": 0, "t": 3}
+ assert sol["t"] == {}
+ assert nx.cost_of_flow(G, sol, weight=1) == 23
+
+ def test_zero_capacity_edges(self):
+ """Address issue raised in ticket #617 by arv."""
+ G = nx.DiGraph()
+ G.add_edges_from(
+ [
+ (1, 2, {"capacity": 1, "weight": 1}),
+ (1, 5, {"capacity": 1, "weight": 1}),
+ (2, 3, {"capacity": 0, "weight": 1}),
+ (2, 5, {"capacity": 1, "weight": 1}),
+ (5, 3, {"capacity": 2, "weight": 1}),
+ (5, 4, {"capacity": 0, "weight": 1}),
+ (3, 4, {"capacity": 2, "weight": 1}),
+ ]
+ )
+ G.nodes[1]["demand"] = -1
+ G.nodes[2]["demand"] = -1
+ G.nodes[4]["demand"] = 2
+
+ flowCost, H = nx.network_simplex(G)
+ soln = {1: {2: 0, 5: 1}, 2: {3: 0, 5: 1}, 3: {4: 2}, 4: {}, 5: {3: 2, 4: 0}}
+ assert flowCost == 6
+ assert nx.min_cost_flow_cost(G) == 6
+ assert H == soln
+ assert nx.min_cost_flow(G) == soln
+ assert nx.cost_of_flow(G, H) == 6
+
+ flowCost, H = nx.capacity_scaling(G)
+ assert flowCost == 6
+ assert H == soln
+ assert nx.cost_of_flow(G, H) == 6
+
+ def test_digon(self):
+ """Check if digons are handled properly. Taken from ticket
+ #618 by arv."""
+ nodes = [(1, {}), (2, {"demand": -4}), (3, {"demand": 4})]
+ edges = [
+ (1, 2, {"capacity": 3, "weight": 600000}),
+ (2, 1, {"capacity": 2, "weight": 0}),
+ (2, 3, {"capacity": 5, "weight": 714285}),
+ (3, 2, {"capacity": 2, "weight": 0}),
+ ]
+ G = nx.DiGraph(edges)
+ G.add_nodes_from(nodes)
+ flowCost, H = nx.network_simplex(G)
+ soln = {1: {2: 0}, 2: {1: 0, 3: 4}, 3: {2: 0}}
+ assert flowCost == 2857140
+ assert nx.min_cost_flow_cost(G) == 2857140
+ assert H == soln
+ assert nx.min_cost_flow(G) == soln
+ assert nx.cost_of_flow(G, H) == 2857140
+
+ flowCost, H = nx.capacity_scaling(G)
+ assert flowCost == 2857140
+ assert H == soln
+ assert nx.cost_of_flow(G, H) == 2857140
+
+ def test_deadend(self):
+ """Check if one-node cycles are handled properly. Taken from ticket
+ #2906 from @sshraven."""
+ G = nx.DiGraph()
+
+ G.add_nodes_from(range(5), demand=0)
+ G.nodes[4]["demand"] = -13
+ G.nodes[3]["demand"] = 13
+
+ G.add_edges_from([(0, 2), (0, 3), (2, 1)], capacity=20, weight=0.1)
+ pytest.raises(nx.NetworkXUnfeasible, nx.min_cost_flow, G)
+
+ def test_infinite_capacity_neg_digon(self):
+ """An infinite capacity negative cost digon results in an unbounded
+ instance."""
+ nodes = [(1, {}), (2, {"demand": -4}), (3, {"demand": 4})]
+ edges = [
+ (1, 2, {"weight": -600}),
+ (2, 1, {"weight": 0}),
+ (2, 3, {"capacity": 5, "weight": 714285}),
+ (3, 2, {"capacity": 2, "weight": 0}),
+ ]
+ G = nx.DiGraph(edges)
+ G.add_nodes_from(nodes)
+ pytest.raises(nx.NetworkXUnbounded, nx.network_simplex, G)
+ pytest.raises(nx.NetworkXUnbounded, nx.capacity_scaling, G)
+
+ def test_finite_capacity_neg_digon(self):
+ """The digon should receive the maximum amount of flow it can handle.
+ Taken from ticket #749 by @chuongdo."""
+ G = nx.DiGraph()
+ G.add_edge("a", "b", capacity=1, weight=-1)
+ G.add_edge("b", "a", capacity=1, weight=-1)
+ min_cost = -2
+ assert nx.min_cost_flow_cost(G) == min_cost
+
+ flowCost, H = nx.capacity_scaling(G)
+ assert flowCost == -2
+ assert H == {"a": {"b": 1}, "b": {"a": 1}}
+ assert nx.cost_of_flow(G, H) == -2
+
+ def test_multidigraph(self):
+ """Multidigraphs are acceptable."""
+ G = nx.MultiDiGraph()
+ G.add_weighted_edges_from([(1, 2, 1), (2, 3, 2)], weight="capacity")
+ flowCost, H = nx.network_simplex(G)
+ assert flowCost == 0
+ assert H == {1: {2: {0: 0}}, 2: {3: {0: 0}}, 3: {}}
+
+ flowCost, H = nx.capacity_scaling(G)
+ assert flowCost == 0
+ assert H == {1: {2: {0: 0}}, 2: {3: {0: 0}}, 3: {}}
+
+ def test_negative_selfloops(self):
+ """Negative selfloops should cause an exception if uncapacitated and
+ always be saturated otherwise.
+ """
+ G = nx.DiGraph()
+ G.add_edge(1, 1, weight=-1)
+ pytest.raises(nx.NetworkXUnbounded, nx.network_simplex, G)
+ pytest.raises(nx.NetworkXUnbounded, nx.capacity_scaling, G)
+ G[1][1]["capacity"] = 2
+ flowCost, H = nx.network_simplex(G)
+ assert flowCost == -2
+ assert H == {1: {1: 2}}
+ flowCost, H = nx.capacity_scaling(G)
+ assert flowCost == -2
+ assert H == {1: {1: 2}}
+
+ G = nx.MultiDiGraph()
+ G.add_edge(1, 1, "x", weight=-1)
+ G.add_edge(1, 1, "y", weight=1)
+ pytest.raises(nx.NetworkXUnbounded, nx.network_simplex, G)
+ pytest.raises(nx.NetworkXUnbounded, nx.capacity_scaling, G)
+ G[1][1]["x"]["capacity"] = 2
+ flowCost, H = nx.network_simplex(G)
+ assert flowCost == -2
+ assert H == {1: {1: {"x": 2, "y": 0}}}
+ flowCost, H = nx.capacity_scaling(G)
+ assert flowCost == -2
+ assert H == {1: {1: {"x": 2, "y": 0}}}
+
+ def test_bone_shaped(self):
+ # From #1283
+ G = nx.DiGraph()
+ G.add_node(0, demand=-4)
+ G.add_node(1, demand=2)
+ G.add_node(2, demand=2)
+ G.add_node(3, demand=4)
+ G.add_node(4, demand=-2)
+ G.add_node(5, demand=-2)
+ G.add_edge(0, 1, capacity=4)
+ G.add_edge(0, 2, capacity=4)
+ G.add_edge(4, 3, capacity=4)
+ G.add_edge(5, 3, capacity=4)
+ G.add_edge(0, 3, capacity=0)
+ flowCost, H = nx.network_simplex(G)
+ assert flowCost == 0
+ assert H == {0: {1: 2, 2: 2, 3: 0}, 1: {}, 2: {}, 3: {}, 4: {3: 2}, 5: {3: 2}}
+ flowCost, H = nx.capacity_scaling(G)
+ assert flowCost == 0
+ assert H == {0: {1: 2, 2: 2, 3: 0}, 1: {}, 2: {}, 3: {}, 4: {3: 2}, 5: {3: 2}}
+
+ def test_exceptions(self):
+ G = nx.Graph()
+ pytest.raises(nx.NetworkXNotImplemented, nx.network_simplex, G)
+ pytest.raises(nx.NetworkXNotImplemented, nx.capacity_scaling, G)
+ G = nx.MultiGraph()
+ pytest.raises(nx.NetworkXNotImplemented, nx.network_simplex, G)
+ pytest.raises(nx.NetworkXNotImplemented, nx.capacity_scaling, G)
+ G = nx.DiGraph()
+ pytest.raises(nx.NetworkXError, nx.network_simplex, G)
+ # pytest.raises(nx.NetworkXError, nx.capacity_scaling, G)
+ G.add_node(0, demand=float("inf"))
+ pytest.raises(nx.NetworkXError, nx.network_simplex, G)
+ pytest.raises(nx.NetworkXUnfeasible, nx.capacity_scaling, G)
+ G.nodes[0]["demand"] = 0
+ G.add_node(1, demand=0)
+ G.add_edge(0, 1, weight=-float("inf"))
+ pytest.raises(nx.NetworkXError, nx.network_simplex, G)
+ pytest.raises(nx.NetworkXUnfeasible, nx.capacity_scaling, G)
+ G[0][1]["weight"] = 0
+ G.add_edge(0, 0, weight=float("inf"))
+ pytest.raises(nx.NetworkXError, nx.network_simplex, G)
+ # pytest.raises(nx.NetworkXError, nx.capacity_scaling, G)
+ G[0][0]["weight"] = 0
+ G[0][1]["capacity"] = -1
+ pytest.raises(nx.NetworkXUnfeasible, nx.network_simplex, G)
+ # pytest.raises(nx.NetworkXUnfeasible, nx.capacity_scaling, G)
+ G[0][1]["capacity"] = 0
+ G[0][0]["capacity"] = -1
+ pytest.raises(nx.NetworkXUnfeasible, nx.network_simplex, G)
+ # pytest.raises(nx.NetworkXUnfeasible, nx.capacity_scaling, G)
+
+ def test_large(self):
+ fname = (
+ importlib.resources.files("networkx.algorithms.flow.tests")
+ / "netgen-2.gpickle.bz2"
+ )
+ with bz2.BZ2File(fname, "rb") as f:
+ G = pickle.load(f)
+ flowCost, flowDict = nx.network_simplex(G)
+ assert 6749969302 == flowCost
+ assert 6749969302 == nx.cost_of_flow(G, flowDict)
+ flowCost, flowDict = nx.capacity_scaling(G)
+ assert 6749969302 == flowCost
+ assert 6749969302 == nx.cost_of_flow(G, flowDict)
diff --git a/.venv/lib/python3.12/site-packages/networkx/algorithms/flow/tests/test_networksimplex.py b/.venv/lib/python3.12/site-packages/networkx/algorithms/flow/tests/test_networksimplex.py
new file mode 100644
index 00000000..5b3b5f6d
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/networkx/algorithms/flow/tests/test_networksimplex.py
@@ -0,0 +1,387 @@
+import bz2
+import importlib.resources
+import os
+import pickle
+
+import pytest
+
+import networkx as nx
+
+
+@pytest.fixture
+def simple_flow_graph():
+ G = nx.DiGraph()
+ G.add_node("a", demand=0)
+ G.add_node("b", demand=-5)
+ G.add_node("c", demand=50000000)
+ G.add_node("d", demand=-49999995)
+ G.add_edge("a", "b", weight=3, capacity=4)
+ G.add_edge("a", "c", weight=6, capacity=10)
+ G.add_edge("b", "d", weight=1, capacity=9)
+ G.add_edge("c", "d", weight=2, capacity=5)
+ return G
+
+
+@pytest.fixture
+def simple_no_flow_graph():
+ G = nx.DiGraph()
+ G.add_node("s", demand=-5)
+ G.add_node("t", demand=5)
+ G.add_edge("s", "a", weight=1, capacity=3)
+ G.add_edge("a", "b", weight=3)
+ G.add_edge("a", "c", weight=-6)
+ G.add_edge("b", "d", weight=1)
+ G.add_edge("c", "d", weight=-2)
+ G.add_edge("d", "t", weight=1, capacity=3)
+ return G
+
+
+def get_flowcost_from_flowdict(G, flowDict):
+ """Returns flow cost calculated from flow dictionary"""
+ flowCost = 0
+ for u in flowDict:
+ for v in flowDict[u]:
+ flowCost += flowDict[u][v] * G[u][v]["weight"]
+ return flowCost
+
+
+def test_infinite_demand_raise(simple_flow_graph):
+ G = simple_flow_graph
+ inf = float("inf")
+ nx.set_node_attributes(G, {"a": {"demand": inf}})
+ pytest.raises(nx.NetworkXError, nx.network_simplex, G)
+
+
+def test_neg_infinite_demand_raise(simple_flow_graph):
+ G = simple_flow_graph
+ inf = float("inf")
+ nx.set_node_attributes(G, {"a": {"demand": -inf}})
+ pytest.raises(nx.NetworkXError, nx.network_simplex, G)
+
+
+def test_infinite_weight_raise(simple_flow_graph):
+ G = simple_flow_graph
+ inf = float("inf")
+ nx.set_edge_attributes(
+ G, {("a", "b"): {"weight": inf}, ("b", "d"): {"weight": inf}}
+ )
+ pytest.raises(nx.NetworkXError, nx.network_simplex, G)
+
+
+def test_nonzero_net_demand_raise(simple_flow_graph):
+ G = simple_flow_graph
+ nx.set_node_attributes(G, {"b": {"demand": -4}})
+ pytest.raises(nx.NetworkXUnfeasible, nx.network_simplex, G)
+
+
+def test_negative_capacity_raise(simple_flow_graph):
+ G = simple_flow_graph
+ nx.set_edge_attributes(G, {("a", "b"): {"weight": 1}, ("b", "d"): {"capacity": -9}})
+ pytest.raises(nx.NetworkXUnfeasible, nx.network_simplex, G)
+
+
+def test_no_flow_satisfying_demands(simple_no_flow_graph):
+ G = simple_no_flow_graph
+ pytest.raises(nx.NetworkXUnfeasible, nx.network_simplex, G)
+
+
+def test_sum_demands_not_zero(simple_no_flow_graph):
+ G = simple_no_flow_graph
+ nx.set_node_attributes(G, {"t": {"demand": 4}})
+ pytest.raises(nx.NetworkXUnfeasible, nx.network_simplex, G)
+
+
+def test_google_or_tools_example():
+ """
+ https://developers.google.com/optimization/flow/mincostflow
+ """
+ G = nx.DiGraph()
+ start_nodes = [0, 0, 1, 1, 1, 2, 2, 3, 4]
+ end_nodes = [1, 2, 2, 3, 4, 3, 4, 4, 2]
+ capacities = [15, 8, 20, 4, 10, 15, 4, 20, 5]
+ unit_costs = [4, 4, 2, 2, 6, 1, 3, 2, 3]
+ supplies = [20, 0, 0, -5, -15]
+ answer = 150
+
+ for i in range(len(supplies)):
+ G.add_node(i, demand=(-1) * supplies[i]) # supplies are negative of demand
+
+ for i in range(len(start_nodes)):
+ G.add_edge(
+ start_nodes[i], end_nodes[i], weight=unit_costs[i], capacity=capacities[i]
+ )
+
+ flowCost, flowDict = nx.network_simplex(G)
+ assert flowCost == answer
+ assert flowCost == get_flowcost_from_flowdict(G, flowDict)
+
+
+def test_google_or_tools_example2():
+ """
+ https://developers.google.com/optimization/flow/mincostflow
+ """
+ G = nx.DiGraph()
+ start_nodes = [0, 0, 1, 1, 1, 2, 2, 3, 4, 3]
+ end_nodes = [1, 2, 2, 3, 4, 3, 4, 4, 2, 5]
+ capacities = [15, 8, 20, 4, 10, 15, 4, 20, 5, 10]
+ unit_costs = [4, 4, 2, 2, 6, 1, 3, 2, 3, 4]
+ supplies = [23, 0, 0, -5, -15, -3]
+ answer = 183
+
+ for i in range(len(supplies)):
+ G.add_node(i, demand=(-1) * supplies[i]) # supplies are negative of demand
+
+ for i in range(len(start_nodes)):
+ G.add_edge(
+ start_nodes[i], end_nodes[i], weight=unit_costs[i], capacity=capacities[i]
+ )
+
+ flowCost, flowDict = nx.network_simplex(G)
+ assert flowCost == answer
+ assert flowCost == get_flowcost_from_flowdict(G, flowDict)
+
+
+def test_large():
+ fname = (
+ importlib.resources.files("networkx.algorithms.flow.tests")
+ / "netgen-2.gpickle.bz2"
+ )
+
+ with bz2.BZ2File(fname, "rb") as f:
+ G = pickle.load(f)
+ flowCost, flowDict = nx.network_simplex(G)
+ assert 6749969302 == flowCost
+ assert 6749969302 == nx.cost_of_flow(G, flowDict)
+
+
+def test_simple_digraph():
+ G = nx.DiGraph()
+ G.add_node("a", demand=-5)
+ G.add_node("d", demand=5)
+ G.add_edge("a", "b", weight=3, capacity=4)
+ G.add_edge("a", "c", weight=6, capacity=10)
+ G.add_edge("b", "d", weight=1, capacity=9)
+ G.add_edge("c", "d", weight=2, capacity=5)
+ flowCost, H = nx.network_simplex(G)
+ soln = {"a": {"b": 4, "c": 1}, "b": {"d": 4}, "c": {"d": 1}, "d": {}}
+ assert flowCost == 24
+ assert nx.min_cost_flow_cost(G) == 24
+ assert H == soln
+
+
+def test_negcycle_infcap():
+ G = nx.DiGraph()
+ G.add_node("s", demand=-5)
+ G.add_node("t", demand=5)
+ G.add_edge("s", "a", weight=1, capacity=3)
+ G.add_edge("a", "b", weight=3)
+ G.add_edge("c", "a", weight=-6)
+ G.add_edge("b", "d", weight=1)
+ G.add_edge("d", "c", weight=-2)
+ G.add_edge("d", "t", weight=1, capacity=3)
+ pytest.raises(nx.NetworkXUnfeasible, nx.network_simplex, G)
+
+
+def test_transshipment():
+ G = nx.DiGraph()
+ G.add_node("a", demand=1)
+ G.add_node("b", demand=-2)
+ G.add_node("c", demand=-2)
+ G.add_node("d", demand=3)
+ G.add_node("e", demand=-4)
+ G.add_node("f", demand=-4)
+ G.add_node("g", demand=3)
+ G.add_node("h", demand=2)
+ G.add_node("r", demand=3)
+ G.add_edge("a", "c", weight=3)
+ G.add_edge("r", "a", weight=2)
+ G.add_edge("b", "a", weight=9)
+ G.add_edge("r", "c", weight=0)
+ G.add_edge("b", "r", weight=-6)
+ G.add_edge("c", "d", weight=5)
+ G.add_edge("e", "r", weight=4)
+ G.add_edge("e", "f", weight=3)
+ G.add_edge("h", "b", weight=4)
+ G.add_edge("f", "d", weight=7)
+ G.add_edge("f", "h", weight=12)
+ G.add_edge("g", "d", weight=12)
+ G.add_edge("f", "g", weight=-1)
+ G.add_edge("h", "g", weight=-10)
+ flowCost, H = nx.network_simplex(G)
+ soln = {
+ "a": {"c": 0},
+ "b": {"a": 0, "r": 2},
+ "c": {"d": 3},
+ "d": {},
+ "e": {"r": 3, "f": 1},
+ "f": {"d": 0, "g": 3, "h": 2},
+ "g": {"d": 0},
+ "h": {"b": 0, "g": 0},
+ "r": {"a": 1, "c": 1},
+ }
+ assert flowCost == 41
+ assert H == soln
+
+
+def test_digraph1():
+ # From Bradley, S. P., Hax, A. C. and Magnanti, T. L. Applied
+ # Mathematical Programming. Addison-Wesley, 1977.
+ G = nx.DiGraph()
+ G.add_node(1, demand=-20)
+ G.add_node(4, demand=5)
+ G.add_node(5, demand=15)
+ G.add_edges_from(
+ [
+ (1, 2, {"capacity": 15, "weight": 4}),
+ (1, 3, {"capacity": 8, "weight": 4}),
+ (2, 3, {"weight": 2}),
+ (2, 4, {"capacity": 4, "weight": 2}),
+ (2, 5, {"capacity": 10, "weight": 6}),
+ (3, 4, {"capacity": 15, "weight": 1}),
+ (3, 5, {"capacity": 5, "weight": 3}),
+ (4, 5, {"weight": 2}),
+ (5, 3, {"capacity": 4, "weight": 1}),
+ ]
+ )
+ flowCost, H = nx.network_simplex(G)
+ soln = {
+ 1: {2: 12, 3: 8},
+ 2: {3: 8, 4: 4, 5: 0},
+ 3: {4: 11, 5: 5},
+ 4: {5: 10},
+ 5: {3: 0},
+ }
+ assert flowCost == 150
+ assert nx.min_cost_flow_cost(G) == 150
+ assert H == soln
+
+
+def test_zero_capacity_edges():
+ """Address issue raised in ticket #617 by arv."""
+ G = nx.DiGraph()
+ G.add_edges_from(
+ [
+ (1, 2, {"capacity": 1, "weight": 1}),
+ (1, 5, {"capacity": 1, "weight": 1}),
+ (2, 3, {"capacity": 0, "weight": 1}),
+ (2, 5, {"capacity": 1, "weight": 1}),
+ (5, 3, {"capacity": 2, "weight": 1}),
+ (5, 4, {"capacity": 0, "weight": 1}),
+ (3, 4, {"capacity": 2, "weight": 1}),
+ ]
+ )
+ G.nodes[1]["demand"] = -1
+ G.nodes[2]["demand"] = -1
+ G.nodes[4]["demand"] = 2
+
+ flowCost, H = nx.network_simplex(G)
+ soln = {1: {2: 0, 5: 1}, 2: {3: 0, 5: 1}, 3: {4: 2}, 4: {}, 5: {3: 2, 4: 0}}
+ assert flowCost == 6
+ assert nx.min_cost_flow_cost(G) == 6
+ assert H == soln
+
+
+def test_digon():
+ """Check if digons are handled properly. Taken from ticket
+ #618 by arv."""
+ nodes = [(1, {}), (2, {"demand": -4}), (3, {"demand": 4})]
+ edges = [
+ (1, 2, {"capacity": 3, "weight": 600000}),
+ (2, 1, {"capacity": 2, "weight": 0}),
+ (2, 3, {"capacity": 5, "weight": 714285}),
+ (3, 2, {"capacity": 2, "weight": 0}),
+ ]
+ G = nx.DiGraph(edges)
+ G.add_nodes_from(nodes)
+ flowCost, H = nx.network_simplex(G)
+ soln = {1: {2: 0}, 2: {1: 0, 3: 4}, 3: {2: 0}}
+ assert flowCost == 2857140
+
+
+def test_deadend():
+ """Check if one-node cycles are handled properly. Taken from ticket
+ #2906 from @sshraven."""
+ G = nx.DiGraph()
+
+ G.add_nodes_from(range(5), demand=0)
+ G.nodes[4]["demand"] = -13
+ G.nodes[3]["demand"] = 13
+
+ G.add_edges_from([(0, 2), (0, 3), (2, 1)], capacity=20, weight=0.1)
+ pytest.raises(nx.NetworkXUnfeasible, nx.network_simplex, G)
+
+
+def test_infinite_capacity_neg_digon():
+ """An infinite capacity negative cost digon results in an unbounded
+ instance."""
+ nodes = [(1, {}), (2, {"demand": -4}), (3, {"demand": 4})]
+ edges = [
+ (1, 2, {"weight": -600}),
+ (2, 1, {"weight": 0}),
+ (2, 3, {"capacity": 5, "weight": 714285}),
+ (3, 2, {"capacity": 2, "weight": 0}),
+ ]
+ G = nx.DiGraph(edges)
+ G.add_nodes_from(nodes)
+ pytest.raises(nx.NetworkXUnbounded, nx.network_simplex, G)
+
+
+def test_multidigraph():
+ """Multidigraphs are acceptable."""
+ G = nx.MultiDiGraph()
+ G.add_weighted_edges_from([(1, 2, 1), (2, 3, 2)], weight="capacity")
+ flowCost, H = nx.network_simplex(G)
+ assert flowCost == 0
+ assert H == {1: {2: {0: 0}}, 2: {3: {0: 0}}, 3: {}}
+
+
+def test_negative_selfloops():
+ """Negative selfloops should cause an exception if uncapacitated and
+ always be saturated otherwise.
+ """
+ G = nx.DiGraph()
+ G.add_edge(1, 1, weight=-1)
+ pytest.raises(nx.NetworkXUnbounded, nx.network_simplex, G)
+
+ G[1][1]["capacity"] = 2
+ flowCost, H = nx.network_simplex(G)
+ assert flowCost == -2
+ assert H == {1: {1: 2}}
+
+ G = nx.MultiDiGraph()
+ G.add_edge(1, 1, "x", weight=-1)
+ G.add_edge(1, 1, "y", weight=1)
+ pytest.raises(nx.NetworkXUnbounded, nx.network_simplex, G)
+
+ G[1][1]["x"]["capacity"] = 2
+ flowCost, H = nx.network_simplex(G)
+ assert flowCost == -2
+ assert H == {1: {1: {"x": 2, "y": 0}}}
+
+
+def test_bone_shaped():
+ # From #1283
+ G = nx.DiGraph()
+ G.add_node(0, demand=-4)
+ G.add_node(1, demand=2)
+ G.add_node(2, demand=2)
+ G.add_node(3, demand=4)
+ G.add_node(4, demand=-2)
+ G.add_node(5, demand=-2)
+ G.add_edge(0, 1, capacity=4)
+ G.add_edge(0, 2, capacity=4)
+ G.add_edge(4, 3, capacity=4)
+ G.add_edge(5, 3, capacity=4)
+ G.add_edge(0, 3, capacity=0)
+ flowCost, H = nx.network_simplex(G)
+ assert flowCost == 0
+ assert H == {0: {1: 2, 2: 2, 3: 0}, 1: {}, 2: {}, 3: {}, 4: {3: 2}, 5: {3: 2}}
+
+
+def test_graphs_type_exceptions():
+ G = nx.Graph()
+ pytest.raises(nx.NetworkXNotImplemented, nx.network_simplex, G)
+ G = nx.MultiGraph()
+ pytest.raises(nx.NetworkXNotImplemented, nx.network_simplex, G)
+ G = nx.DiGraph()
+ pytest.raises(nx.NetworkXError, nx.network_simplex, G)
diff --git a/.venv/lib/python3.12/site-packages/networkx/algorithms/flow/tests/wlm3.gpickle.bz2 b/.venv/lib/python3.12/site-packages/networkx/algorithms/flow/tests/wlm3.gpickle.bz2
new file mode 100644
index 00000000..8ce935a8
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/networkx/algorithms/flow/tests/wlm3.gpickle.bz2
Binary files differ