/usr/lib/python2.7/dist-packages/networkx/algorithms/connectivity/tests/test_cuts.py is in python-networkx 1.9+dfsg1-1.
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import networkx as nx
# Flow functions to use in tests.
# We do not test legacy ford_fulkerson implementation: it's too slow.
from networkx.algorithms.flow import (edmonds_karp, preflow_push,
shortest_augmenting_path)
flow_funcs = [edmonds_karp, preflow_push, shortest_augmenting_path]
# import connectivity functions not in base namespace
from networkx.algorithms.connectivity import (minimum_st_edge_cut,
minimum_st_node_cut)
msg = "Assertion failed in function: {0}"
# Tests for node and edge cutsets
def _generate_no_biconnected(max_attempts=50):
attempts = 0
while True:
G = nx.fast_gnp_random_graph(100,0.0575)
if nx.is_connected(G) and not nx.is_biconnected(G):
attempts = 0
yield G
else:
if attempts >= max_attempts:
msg = "Tried %d times: no suitable Graph."%attempts
raise Exception(msg % max_attempts)
else:
attempts += 1
def test_articulation_points():
Ggen = _generate_no_biconnected()
for flow_func in flow_funcs:
for i in range(3):
G = next(Ggen)
cut = nx.minimum_node_cut(G, flow_func=flow_func)
assert_true(len(cut) == 1, msg=msg.format(flow_func.__name__))
assert_true(cut.pop() in set(nx.articulation_points(G)),
msg=msg.format(flow_func.__name__))
def test_brandes_erlebach_book():
# Figure 1 chapter 7: Connectivity
# http://www.informatik.uni-augsburg.de/thi/personen/kammer/Graph_Connectivity.pdf
G = nx.Graph()
G.add_edges_from([(1, 2), (1, 3), (1, 4), (1, 5), (2, 3), (2, 6), (3, 4),
(3, 6), (4, 6), (4, 7), (5, 7), (6, 8), (6, 9), (7, 8),
(7, 10), (8, 11), (9, 10), (9, 11), (10, 11)])
for flow_func in flow_funcs:
kwargs = dict(flow_func=flow_func)
# edge cutsets
assert_equal(3, len(nx.minimum_edge_cut(G, 1, 11, **kwargs)),
msg=msg.format(flow_func.__name__))
edge_cut = nx.minimum_edge_cut(G, **kwargs)
# Node 5 has only two edges
assert_equal(2, len(edge_cut), msg=msg.format(flow_func.__name__))
H = G.copy()
H.remove_edges_from(edge_cut)
assert_false(nx.is_connected(H), msg=msg.format(flow_func.__name__))
# node cuts
assert_equal(set([6, 7]), minimum_st_node_cut(G, 1, 11, **kwargs),
msg=msg.format(flow_func.__name__))
assert_equal(set([6, 7]), nx.minimum_node_cut(G, 1, 11, **kwargs),
msg=msg.format(flow_func.__name__))
node_cut = nx.minimum_node_cut(G, **kwargs)
assert_equal(2, len(node_cut), msg=msg.format(flow_func.__name__))
H = G.copy()
H.remove_nodes_from(node_cut)
assert_false(nx.is_connected(H), msg=msg.format(flow_func.__name__))
def test_white_harary_paper():
# Figure 1b white and harary (2001)
# http://eclectic.ss.uci.edu/~drwhite/sm-w23.PDF
# A graph with high adhesion (edge connectivity) and low cohesion
# (node connectivity)
G = nx.disjoint_union(nx.complete_graph(4), nx.complete_graph(4))
G.remove_node(7)
for i in range(4,7):
G.add_edge(0,i)
G = nx.disjoint_union(G, nx.complete_graph(4))
G.remove_node(G.order()-1)
for i in range(7,10):
G.add_edge(0,i)
for flow_func in flow_funcs:
kwargs = dict(flow_func=flow_func)
# edge cuts
edge_cut = nx.minimum_edge_cut(G, **kwargs)
assert_equal(3, len(edge_cut), msg=msg.format(flow_func.__name__))
H = G.copy()
H.remove_edges_from(edge_cut)
assert_false(nx.is_connected(H), msg=msg.format(flow_func.__name__))
# node cuts
node_cut = nx.minimum_node_cut(G, **kwargs)
assert_equal(set([0]), node_cut, msg=msg.format(flow_func.__name__))
H = G.copy()
H.remove_nodes_from(node_cut)
assert_false(nx.is_connected(H), msg=msg.format(flow_func.__name__))
def test_petersen_cutset():
G = nx.petersen_graph()
for flow_func in flow_funcs:
kwargs = dict(flow_func=flow_func)
# edge cuts
edge_cut = nx.minimum_edge_cut(G, **kwargs)
assert_equal(3, len(edge_cut), msg=msg.format(flow_func.__name__))
H = G.copy()
H.remove_edges_from(edge_cut)
assert_false(nx.is_connected(H), msg=msg.format(flow_func.__name__))
# node cuts
node_cut = nx.minimum_node_cut(G, **kwargs)
assert_equal(3, len(node_cut), msg=msg.format(flow_func.__name__))
H = G.copy()
H.remove_nodes_from(node_cut)
assert_false(nx.is_connected(H), msg=msg.format(flow_func.__name__))
def test_octahedral_cutset():
G=nx.octahedral_graph()
for flow_func in flow_funcs:
kwargs = dict(flow_func=flow_func)
# edge cuts
edge_cut = nx.minimum_edge_cut(G, **kwargs)
assert_equal(4, len(edge_cut), msg=msg.format(flow_func.__name__))
H = G.copy()
H.remove_edges_from(edge_cut)
assert_false(nx.is_connected(H), msg=msg.format(flow_func.__name__))
# node cuts
node_cut = nx.minimum_node_cut(G, **kwargs)
assert_equal(4, len(node_cut), msg=msg.format(flow_func.__name__))
H = G.copy()
H.remove_nodes_from(node_cut)
assert_false(nx.is_connected(H), msg=msg.format(flow_func.__name__))
def test_icosahedral_cutset():
G=nx.icosahedral_graph()
for flow_func in flow_funcs:
kwargs = dict(flow_func=flow_func)
# edge cuts
edge_cut = nx.minimum_edge_cut(G, **kwargs)
assert_equal(5, len(edge_cut), msg=msg.format(flow_func.__name__))
H = G.copy()
H.remove_edges_from(edge_cut)
assert_false(nx.is_connected(H), msg=msg.format(flow_func.__name__))
# node cuts
node_cut = nx.minimum_node_cut(G, **kwargs)
assert_equal(5, len(node_cut), msg=msg.format(flow_func.__name__))
H = G.copy()
H.remove_nodes_from(node_cut)
assert_false(nx.is_connected(H), msg=msg.format(flow_func.__name__))
def test_node_cutset_exception():
G=nx.Graph()
G.add_edges_from([(1, 2), (3, 4)])
for flow_func in flow_funcs:
assert_raises(nx.NetworkXError, nx.minimum_node_cut, G, flow_func=flow_func)
def test_node_cutset_random_graphs():
for flow_func in flow_funcs:
for i in range(3):
G = nx.fast_gnp_random_graph(50, 0.25)
if not nx.is_connected(G):
ccs = iter(nx.connected_components(G))
start = next(ccs)[0]
G.add_edges_from((start, c[0]) for c in ccs)
cutset = nx.minimum_node_cut(G, flow_func=flow_func)
assert_equal(nx.node_connectivity(G), len(cutset),
msg=msg.format(flow_func.__name__))
G.remove_nodes_from(cutset)
assert_false(nx.is_connected(G), msg=msg.format(flow_func.__name__))
def test_edge_cutset_random_graphs():
for flow_func in flow_funcs:
for i in range(3):
G = nx.fast_gnp_random_graph(50, 0.25)
if not nx.is_connected(G):
ccs = iter(nx.connected_components(G))
start = next(ccs)[0]
G.add_edges_from( (start,c[0]) for c in ccs )
cutset = nx.minimum_edge_cut(G, flow_func=flow_func)
assert_equal(nx.edge_connectivity(G), len(cutset),
msg=msg.format(flow_func.__name__))
G.remove_edges_from(cutset)
assert_false(nx.is_connected(G), msg=msg.format(flow_func.__name__))
def test_empty_graphs():
G = nx.Graph()
D = nx.DiGraph()
for interface_func in [nx.minimum_node_cut, nx.minimum_edge_cut]:
for flow_func in flow_funcs:
assert_raises(nx.NetworkXPointlessConcept, interface_func, G,
flow_func=flow_func)
assert_raises(nx.NetworkXPointlessConcept, interface_func, D,
flow_func=flow_func)
def test_unbounded():
G = nx.complete_graph(5)
for flow_func in flow_funcs:
assert_equal(4, len(minimum_st_edge_cut(G, 1, 4, flow_func=flow_func)))
def test_missing_source():
G = nx.path_graph(4)
for interface_func in [nx.minimum_edge_cut, nx.minimum_node_cut]:
for flow_func in flow_funcs:
assert_raises(nx.NetworkXError, interface_func, G, 10, 1,
flow_func=flow_func)
def test_missing_target():
G = nx.path_graph(4)
for interface_func in [nx.minimum_edge_cut, nx.minimum_node_cut]:
for flow_func in flow_funcs:
assert_raises(nx.NetworkXError, interface_func, G, 1, 10,
flow_func=flow_func)
def test_not_weakly_connected():
G = nx.DiGraph()
G.add_path([1, 2, 3])
G.add_path([4, 5])
for interface_func in [nx.minimum_edge_cut, nx.minimum_node_cut]:
for flow_func in flow_funcs:
assert_raises(nx.NetworkXError, interface_func, G,
flow_func=flow_func)
def test_not_connected():
G = nx.Graph()
G.add_path([1, 2, 3])
G.add_path([4, 5])
for interface_func in [nx.minimum_edge_cut, nx.minimum_node_cut]:
for flow_func in flow_funcs:
assert_raises(nx.NetworkXError, interface_func, G,
flow_func=flow_func)
def tests_min_cut_complete():
G = nx.complete_graph(5)
for interface_func in [nx.minimum_edge_cut, nx.minimum_node_cut]:
for flow_func in flow_funcs:
assert_equal(4, len(interface_func(G, flow_func=flow_func)))
def tests_min_cut_complete_directed():
G = nx.complete_graph(5)
G = G.to_directed()
for interface_func in [nx.minimum_edge_cut, nx.minimum_node_cut]:
for flow_func in flow_funcs:
assert_equal(4, len(interface_func(G, flow_func=flow_func)))
def test_invalid_auxiliary():
G = nx.complete_graph(5)
assert_raises(nx.NetworkXError, minimum_st_node_cut, G, 0, 3,
auxiliary=G)
def test_interface_only_source():
G = nx.complete_graph(5)
for interface_func in [nx.minimum_node_cut, nx.minimum_edge_cut]:
assert_raises(nx.NetworkXError, interface_func, G, s=0)
def test_interface_only_target():
G = nx.complete_graph(5)
for interface_func in [nx.minimum_node_cut, nx.minimum_edge_cut]:
assert_raises(nx.NetworkXError, interface_func, G, t=3)
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