def test_triangles():
paths = [
(11, 12, 13, 11), # first 3-clique
(21, 22, 23, 21), # second 3-clique
(11, 21), # connected by an edge
]
G = nx.Graph(it.chain(*[pairwise(path) for path in paths]))
# subgraph and ccs are the same in all cases here
assert_equal(
fset(nx.k_edge_components(G, k=1)),
fset(nx.k_edge_subgraphs(G, k=1))
)
assert_equal(
fset(nx.k_edge_components(G, k=2)),
fset(nx.k_edge_subgraphs(G, k=2))
)
assert_equal(
fset(nx.k_edge_components(G, k=3)),
fset(nx.k_edge_subgraphs(G, k=3))
)
_check_edge_connectivity(G)
def test_five_clique():
# Make a graph that can be disconnected less than 4 edges, but no node has
# degree less than 4.
G = nx.disjoint_union(nx.complete_graph(5), nx.complete_graph(5))
paths = [
# add aux-connections
(1, 100, 6),
(2, 100, 7),
(3, 200, 8),
(4, 200, 100),
]
G.add_edges_from(it.chain(*[pairwise(path) for path in paths]))
assert min(dict(nx.degree(G)).values()) == 4
# For k=3 they are the same
assert fset(nx.k_edge_components(G,
k=3)) == fset(nx.k_edge_subgraphs(G, k=3))
# For k=4 they are the different
# the aux nodes are in the same CC as clique 1 but no the same subgraph
assert fset(nx.k_edge_components(G, k=4)) != fset(
nx.k_edge_subgraphs(G, k=4))
# For k=5 they are not the same
assert fset(nx.k_edge_components(G, k=5)) != fset(
nx.k_edge_subgraphs(G, k=5))
# For k=6 they are the same
assert fset(nx.k_edge_components(G,
k=6)) == fset(nx.k_edge_subgraphs(G, k=6))
_check_edge_connectivity(G)
def test_local_subgraph_difference_directed():
dipaths = [
(1, 2, 3, 4, 1),
(1, 3, 1),
]
G = nx.DiGraph(it.chain(*[pairwise(path) for path in dipaths]))
assert_equal(
fset(nx.k_edge_components(G, k=1)),
fset(nx.k_edge_subgraphs(G, k=1))
)
# Unlike undirected graphs, when k=2, for directed graphs there is a case
# where the k-edge-ccs are not the same as the k-edge-subgraphs.
# (in directed graphs ccs and subgraphs are the same when k=2)
assert_not_equal(
fset(nx.k_edge_components(G, k=2)),
fset(nx.k_edge_subgraphs(G, k=2))
)
assert_equal(
fset(nx.k_edge_components(G, k=3)),
fset(nx.k_edge_subgraphs(G, k=3))
)
_check_edge_connectivity(G)
def test_triangles():
paths = [
(11, 12, 13, 11), # first 3-clique
(21, 22, 23, 21), # second 3-clique
(11, 21), # connected by an edge
]
G = nx.Graph(it.chain(*[pairwise(path) for path in paths]))
# subgraph and ccs are the same in all cases here
assert_equal(
fset(nx.k_edge_components(G, k=1)),
fset(nx.k_edge_subgraphs(G, k=1))
)
assert_equal(
fset(nx.k_edge_components(G, k=2)),
fset(nx.k_edge_subgraphs(G, k=2))
)
assert_equal(
fset(nx.k_edge_components(G, k=3)),
fset(nx.k_edge_subgraphs(G, k=3))
)
_check_edge_connectivity(G)
def test_local_subgraph_difference_directed():
dipaths = [
(1, 2, 3, 4, 1),
(1, 3, 1),
]
G = nx.DiGraph(it.chain(*[pairwise(path) for path in dipaths]))
assert_equal(
fset(nx.k_edge_components(G, k=1)),
fset(nx.k_edge_subgraphs(G, k=1))
)
# Unlike undirected graphs, when k=2, for directed graphs there is a case
# where the k-edge-ccs are not the same as the k-edge-subgraphs.
# (in directed graphs ccs and subgraphs are the same when k=2)
assert_not_equal(
fset(nx.k_edge_components(G, k=2)),
fset(nx.k_edge_subgraphs(G, k=2))
)
assert_equal(
fset(nx.k_edge_components(G, k=3)),
fset(nx.k_edge_subgraphs(G, k=3))
)
_check_edge_connectivity(G)
def test_empty_input():
G = nx.Graph()
assert [] == list(nx.k_edge_components(G, k=5))
assert [] == list(nx.k_edge_subgraphs(G, k=5))
G = nx.DiGraph()
assert [] == list(nx.k_edge_components(G, k=5))
assert [] == list(nx.k_edge_subgraphs(G, k=5))
def test_empty_input():
G = nx.Graph()
assert_equal([], list(nx.k_edge_components(G, k=5)))
assert_equal([], list(nx.k_edge_subgraphs(G, k=5)))
G = nx.DiGraph()
assert_equal([], list(nx.k_edge_components(G, k=5)))
assert_equal([], list(nx.k_edge_subgraphs(G, k=5)))
def test_four_clique():
paths = [
(11, 12, 13, 14, 11, 13, 14, 12), # first 4-clique
(21, 22, 23, 24, 21, 23, 24, 22), # second 4-clique
# paths connecting the 4 cliques such that they are
# 3-connected in G, but not in the subgraph.
# Case where the nodes bridging them do not have degree less than 3.
(100, 13),
(12, 100, 22),
(13, 200, 23),
(14, 300, 24),
]
G = nx.Graph(it.chain(*[pairwise(path) for path in paths]))
# The subgraphs and ccs are different for k=3
local_ccs = fset(nx.k_edge_components(G, k=3))
subgraphs = fset(nx.k_edge_subgraphs(G, k=3))
assert local_ccs != subgraphs
# The cliques ares in the same cc
clique1 = frozenset(paths[0])
clique2 = frozenset(paths[1])
assert clique1.union(clique2).union({100}) in local_ccs
# but different subgraphs
assert clique1 in subgraphs
assert clique2 in subgraphs
assert G.degree(100) == 3
_check_edge_connectivity(G)
def test_four_clique():
paths = [
(11, 12, 13, 14, 11, 13, 14, 12), # first 4-clique
(21, 22, 23, 24, 21, 23, 24, 22), # second 4-clique
# paths connecting the 4 cliques such that they are
# 3-connected in G, but not in the subgraph.
# Case where the nodes bridging them do not have degree less than 3.
(100, 13),
(12, 100, 22),
(13, 200, 23),
(14, 300, 24),
]
G = nx.Graph(it.chain(*[pairwise(path) for path in paths]))
# The subgraphs and ccs are different for k=3
local_ccs = fset(nx.k_edge_components(G, k=3))
subgraphs = fset(nx.k_edge_subgraphs(G, k=3))
assert_not_equal(local_ccs, subgraphs)
# The cliques ares in the same cc
clique1 = frozenset(paths[0])
clique2 = frozenset(paths[1])
assert_in(clique1.union(clique2).union({100}), local_ccs)
# but different subgraphs
assert_in(clique1, subgraphs)
assert_in(clique2, subgraphs)
assert_equal(G.degree(100), 3)
_check_edge_connectivity(G)
def get_k_connected_routers(self, k):
graph = self.to_undirected()
components = nx.k_edge_components(graph, k=k)
k_connected_pairs = set()
for component in components:
for r1, r2 in itertools.combinations(component, 2):
if r1 < r2:
k_connected_pairs.add((r1, r2))
else:
k_connected_pairs.add((r2, r1))
return k_connected_pairs
def test_five_clique():
# Make a graph that can be disconnected less than 4 edges, but no node has
# degree less than 4.
G = nx.disjoint_union(nx.complete_graph(5), nx.complete_graph(5))
paths = [
# add aux-connections
(1, 100, 6), (2, 100, 7), (3, 200, 8), (4, 200, 100),
]
G.add_edges_from(it.chain(*[pairwise(path) for path in paths]))
assert_equal(min(dict(nx.degree(G)).values()), 4)
# For k=3 they are the same
assert_equal(
fset(nx.k_edge_components(G, k=3)),
fset(nx.k_edge_subgraphs(G, k=3))
)
# For k=4 they are the different
# the aux nodes are in the same CC as clique 1 but no the same subgraph
assert_not_equal(
fset(nx.k_edge_components(G, k=4)),
fset(nx.k_edge_subgraphs(G, k=4))
)
# For k=5 they are not the same
assert_not_equal(
fset(nx.k_edge_components(G, k=5)),
fset(nx.k_edge_subgraphs(G, k=5))
)
# For k=6 they are the same
assert_equal(
fset(nx.k_edge_components(G, k=6)),
fset(nx.k_edge_subgraphs(G, k=6))
)
_check_edge_connectivity(G)