def test_directed_aux_graph():
# Graph similar to the one in
# http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0136264
a, b, c, d, e, f, g, h, i = "abcdefghi"
dipaths = [
(a, d, b, f, c),
(a, e, b),
(a, e, b, c, g, b, a),
(c, b),
(f, g, f),
(h, i),
]
G = nx.DiGraph(it.chain(*[pairwise(path) for path in dipaths]))
aux_graph = EdgeComponentAuxGraph.construct(G)
components_1 = fset(aux_graph.k_edge_subgraphs(k=1))
target_1 = fset([{a, b, c, d, e, f, g}, {h}, {i}])
assert target_1 == components_1
# Check that the directed case for k=1 agrees with SCCs
alt_1 = fset(nx.strongly_connected_components(G))
assert alt_1 == components_1
components_2 = fset(aux_graph.k_edge_subgraphs(k=2))
target_2 = fset([{i}, {e}, {d}, {b, c, f, g}, {h}, {a}])
assert target_2 == components_2
components_3 = fset(aux_graph.k_edge_subgraphs(k=3))
target_3 = fset([{a}, {b}, {c}, {d}, {e}, {f}, {g}, {h}, {i}])
assert target_3 == components_3
def test_undirected_aux_graph():
# Graph similar to the one in
# http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0136264
a, b, c, d, e, f, g, h, i = 'abcdefghi'
paths = [(a, d, b, f, c), (a, e, b), (a, e, b, c, g, b, a), (c, b),
(f, g, f), (h, i)]
G = nx.Graph(it.chain(*[pairwise(path) for path in paths]))
aux_graph = EdgeComponentAuxGraph.construct(G)
components_1 = fset(aux_graph.k_edge_subgraphs(k=1))
target_1 = fset([{a, b, c, d, e, f, g}, {h, i}])
assert_equal(target_1, components_1)
# Check that the undirected case for k=1 agrees with CCs
alt_1 = fset(nx.k_edge_subgraphs(G, k=1))
assert_equal(alt_1, components_1)
components_2 = fset(aux_graph.k_edge_subgraphs(k=2))
target_2 = fset([{a, b, c, d, e, f, g}, {h}, {i}])
assert_equal(target_2, components_2)
# Check that the undirected case for k=2 agrees with bridge components
alt_2 = fset(nx.k_edge_subgraphs(G, k=2))
assert_equal(alt_2, components_2)
components_3 = fset(aux_graph.k_edge_subgraphs(k=3))
target_3 = fset([{a}, {b, c, f, g}, {d}, {e}, {h}, {i}])
assert_equal(target_3, components_3)
components_4 = fset(aux_graph.k_edge_subgraphs(k=4))
target_4 = fset([{a}, {b}, {c}, {d}, {e}, {f}, {g}, {h}, {i}])
assert_equal(target_4, components_4)
_check_edge_connectivity(G)
def test_local_subgraph_difference():
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 each node of the 4 cliques
(11, 101, 21),
(12, 102, 22),
(13, 103, 23),
(14, 104, 24),
]
G = nx.Graph(it.chain(*[pairwise(path) for path in paths]))
aux_graph = EdgeComponentAuxGraph.construct(G)
# Each clique is returned separately in k-edge-subgraphs
subgraph_ccs = fset(aux_graph.k_edge_subgraphs(3))
subgraph_target = fset([{101}, {102}, {103}, {104}, {21, 22, 23, 24},
{11, 12, 13, 14}])
assert subgraph_ccs == subgraph_target
# But in k-edge-ccs they are returned together
# because they are locally 3-edge-connected
local_ccs = fset(aux_graph.k_edge_components(3))
local_target = fset([{101}, {102}, {103}, {104},
{11, 12, 13, 14, 21, 22, 23, 24}])
assert local_ccs == local_target
def test_directed_aux_graph():
# Graph similar to the one in
# http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0136264
a, b, c, d, e, f, g, h, i = 'abcdefghi'
dipaths = [
(a, d, b, f, c),
(a, e, b),
(a, e, b, c, g, b, a),
(c, b),
(f, g, f),
(h, i)
]
G = nx.DiGraph(it.chain(*[pairwise(path) for path in dipaths]))
aux_graph = EdgeComponentAuxGraph.construct(G)
components_1 = fset(aux_graph.k_edge_subgraphs(k=1))
target_1 = fset([{a, b, c, d, e, f, g}, {h}, {i}])
assert_equal(target_1, components_1)
# Check that the directed case for k=1 agrees with SCCs
alt_1 = fset(nx.strongly_connected_components(G))
assert_equal(alt_1, components_1)
components_2 = fset(aux_graph.k_edge_subgraphs(k=2))
target_2 = fset([{i}, {e}, {d}, {b, c, f, g}, {h}, {a}])
assert_equal(target_2, components_2)
components_3 = fset(aux_graph.k_edge_subgraphs(k=3))
target_3 = fset([{a}, {b}, {c}, {d}, {e}, {f}, {g}, {h}, {i}])
assert_equal(target_3, components_3)
def test_local_subgraph_difference():
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 each node of the 4 cliques
(11, 101, 21),
(12, 102, 22),
(13, 103, 23),
(14, 104, 24),
]
G = nx.Graph(it.chain(*[pairwise(path) for path in paths]))
aux_graph = EdgeComponentAuxGraph.construct(G)
# Each clique is returned separately in k-edge-subgraphs
subgraph_ccs = fset(aux_graph.k_edge_subgraphs(3))
subgraph_target = fset([{101}, {102}, {103}, {104},
{21, 22, 23, 24}, {11, 12, 13, 14}])
assert_equal(subgraph_ccs, subgraph_target)
# But in k-edge-ccs they are returned together
# because they are locally 3-edge-connected
local_ccs = fset(aux_graph.k_edge_components(3))
local_target = fset([{101}, {102}, {103}, {104},
{11, 12, 13, 14, 21, 22, 23, 24}])
assert_equal(local_ccs, local_target)
def test_directed_aux_graph():
# Graph similar to the one in
# http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0136264
a, b, c, d, e, f, g, h, i = 'abcdefghi'
dipaths = [
(a, d, b, f, c),
(a, e, b),
(a, e, b, c, g, b, a),
(c, b),
(f, g, f),
(h, i)
]
G = nx.DiGraph(it.chain(*[pairwise(path) for path in dipaths]))
aux_graph = EdgeComponentAuxGraph.construct(G)
components_1 = fset(aux_graph.k_edge_subgraphs(k=1))
target_1 = fset([set([a, b, c, d, e, f, g]), set([h]), set([i])])
assert_equal(target_1, components_1)
# Check that the directed case for k=1 agrees with SCCs
alt_1 = fset(nx.strongly_connected_components(G))
assert_equal(alt_1, components_1)
components_2 = fset(aux_graph.k_edge_subgraphs(k=2))
target_2 = fset([set([i]), set([e]), set([d]), set([b, c, f, g]), set([h]), set([a])])
assert_equal(target_2, components_2)
components_3 = fset(aux_graph.k_edge_subgraphs(k=3))
target_3 = fset([set([a]), set([b]), set([c]), set([d]), set([e]), set([f]), set([g]), set([h]), set([i])])
assert_equal(target_3, components_3)
def _check_edge_connectivity(G):
"""
Helper - generates all k-edge-components using the aux graph. Checks the
both local and subgraph edge connectivity of each cc. Also checks that
alternate methods of computing the k-edge-ccs generate the same result.
"""
# Construct the auxillary graph that can be used to make each k-cc or k-sub
aux_graph = EdgeComponentAuxGraph.construct(G)
# memoize the local connectivity in this graph
memo = {}
for k in it.count(1):
# Test "local" k-edge-components and k-edge-subgraphs
ccs_local = fset(aux_graph.k_edge_components(k))
ccs_subgraph = fset(aux_graph.k_edge_subgraphs(k))
# Check connectivity properties that should be garuenteed by the
# algorithms.
_assert_local_cc_edge_connectivity(G, ccs_local, k, memo)
_assert_subgraph_edge_connectivity(G, ccs_subgraph, k)
if k == 1 or k == 2 and not G.is_directed():
assert_equal(
ccs_local, ccs_subgraph,
'Subgraphs and components should be the same '
'when k == 1 or (k == 2 and not G.directed())')
if G.is_directed():
# Test special case methods are the same as the aux graph
if k == 1:
alt_sccs = fset(nx.strongly_connected_components(G))
assert_equal(alt_sccs, ccs_local, 'k=1 failed alt')
assert_equal(alt_sccs, ccs_subgraph, 'k=1 failed alt')
else:
# Test special case methods are the same as the aux graph
if k == 1:
alt_ccs = fset(nx.connected_components(G))
assert_equal(alt_ccs, ccs_local, 'k=1 failed alt')
assert_equal(alt_ccs, ccs_subgraph, 'k=1 failed alt')
elif k == 2:
alt_bridge_ccs = fset(bridge_components(G))
assert_equal(alt_bridge_ccs, ccs_local, 'k=2 failed alt')
assert_equal(alt_bridge_ccs, ccs_subgraph, 'k=2 failed alt')
# if new methods for k == 3 or k == 4 are implemented add them here
# Check the general subgraph method works by itself
alt_subgraph_ccs = fset(
[set(C.nodes()) for C in general_k_edge_subgraphs(G, k=k)])
assert_equal(alt_subgraph_ccs, ccs_subgraph,
'alt subgraph method failed')
# Stop once k is larger than all special case methods
# and we cannot break down ccs any further.
if k > 2 and all(len(cc) == 1 for cc in ccs_local):
break
def _check_edge_connectivity(G):
"""
Helper - generates all k-edge-components using the aux graph. Checks the
both local and subgraph edge connectivity of each cc. Also checks that
alternate methods of computing the k-edge-ccs generate the same result.
"""
# Construct the auxiliary graph that can be used to make each k-cc or k-sub
aux_graph = EdgeComponentAuxGraph.construct(G)
# memoize the local connectivity in this graph
memo = {}
for k in it.count(1):
# Test "local" k-edge-components and k-edge-subgraphs
ccs_local = fset(aux_graph.k_edge_components(k))
ccs_subgraph = fset(aux_graph.k_edge_subgraphs(k))
# Check connectivity properties that should be garuenteed by the
# algorithms.
_assert_local_cc_edge_connectivity(G, ccs_local, k, memo)
_assert_subgraph_edge_connectivity(G, ccs_subgraph, k)
if k == 1 or k == 2 and not G.is_directed():
assert_equal(ccs_local, ccs_subgraph,
'Subgraphs and components should be the same '
'when k == 1 or (k == 2 and not G.directed())')
if G.is_directed():
# Test special case methods are the same as the aux graph
if k == 1:
alt_sccs = fset(nx.strongly_connected_components(G))
assert_equal(alt_sccs, ccs_local, 'k=1 failed alt')
assert_equal(alt_sccs, ccs_subgraph, 'k=1 failed alt')
else:
# Test special case methods are the same as the aux graph
if k == 1:
alt_ccs = fset(nx.connected_components(G))
assert_equal(alt_ccs, ccs_local, 'k=1 failed alt')
assert_equal(alt_ccs, ccs_subgraph, 'k=1 failed alt')
elif k == 2:
alt_bridge_ccs = fset(bridge_components(G))
assert_equal(alt_bridge_ccs, ccs_local, 'k=2 failed alt')
assert_equal(alt_bridge_ccs, ccs_subgraph, 'k=2 failed alt')
# if new methods for k == 3 or k == 4 are implemented add them here
# Check the general subgraph method works by itself
alt_subgraph_ccs = fset([set(C.nodes()) for C in
general_k_edge_subgraphs(G, k=k)])
assert_equal(alt_subgraph_ccs, ccs_subgraph,
'alt subgraph method failed')
# Stop once k is larger than all special case methods
# and we cannot break down ccs any further.
if k > 2 and all(len(cc) == 1 for cc in ccs_local):
break
def test_zero_k_exception():
G = nx.Graph()
# functions that return generators error immediately
pytest.raises(ValueError, nx.k_edge_components, G, k=0)
pytest.raises(ValueError, nx.k_edge_subgraphs, G, k=0)
# actual generators only error when you get the first item
aux_graph = EdgeComponentAuxGraph.construct(G)
pytest.raises(ValueError, list, aux_graph.k_edge_components(k=0))
pytest.raises(ValueError, list, aux_graph.k_edge_subgraphs(k=0))
pytest.raises(ValueError, list, general_k_edge_subgraphs(G, k=0))
def test_zero_k_exception():
G = nx.Graph()
# functions that return generators error immediately
assert_raises(ValueError, nx.k_edge_components, G, k=0)
assert_raises(ValueError, nx.k_edge_subgraphs, G, k=0)
# actual generators only error when you get the first item
aux_graph = EdgeComponentAuxGraph.construct(G)
assert_raises(ValueError, list, aux_graph.k_edge_components(k=0))
assert_raises(ValueError, list, aux_graph.k_edge_subgraphs(k=0))
assert_raises(ValueError, list, general_k_edge_subgraphs(G, k=0))