def test_connected_raise():
DG = nx.DiGraph()
with pytest.raises(NetworkXNotImplemented):
next(nx.biconnected_components(DG))
with pytest.raises(NetworkXNotImplemented):
next(nx.biconnected_component_edges(DG))
with pytest.raises(NetworkXNotImplemented):
next(nx.articulation_points(DG))
pytest.raises(NetworkXNotImplemented, nx.is_biconnected, DG)
def test_biconnected_components2():
G=nx.Graph()
nx.add_cycle(G, 'ABC')
nx.add_cycle(G, 'CDE')
nx.add_cycle(G, 'FIJHG')
nx.add_cycle(G, 'GIJ')
G.add_edge('E','G')
comps = list(nx.biconnected_component_edges(G))
answer = [
[tuple('GF'), tuple('FI'), tuple('IG'), tuple('IJ'),
tuple('JG'), tuple('JH'), tuple('HG')],
[tuple('EG')],
[tuple('CD'), tuple('DE'), tuple('CE')],
[tuple('AB'), tuple('BC'), tuple('AC')]
]
assert_components_edges_equal(comps, answer)
def test_biconnected_components2():
G = nx.Graph()
nx.add_cycle(G, 'ABC')
nx.add_cycle(G, 'CDE')
nx.add_cycle(G, 'FIJHG')
nx.add_cycle(G, 'GIJ')
G.add_edge('E', 'G')
comps = list(nx.biconnected_component_edges(G))
answer = [
[tuple('GF'), tuple('FI'), tuple('IG'), tuple('IJ'),
tuple('JG'), tuple('JH'), tuple('HG')],
[tuple('EG')],
[tuple('CD'), tuple('DE'), tuple('CE')],
[tuple('AB'), tuple('BC'), tuple('AC')]
]
assert_components_edges_equal(comps, answer)
def _compute_biconnected_components_edges(
G: nx.Graph) -> List[List[Tuple[int], Set[int]]]:
"""
Biconnected components are maximal subgraphs such that the removal of a node (and all edges incident on that node) will not disconnect the subgraph.
Source:
- https://networkx.github.io/documentation/stable/_modules/networkx/algorithms/components/biconnected.html#biconnected_components
- https://networkx.github.io/documentation/stable/_modules/networkx/algorithms/components/biconnected.html#biconnected_component_edges
------------------
Returns a list of lists of length 2: [Set, List of tuple pairs (edges)]
"""
biconnected_components = list(nx.biconnected_components(G))
biconnected_edges = list(nx.biconnected_component_edges(G))
components_and_edges = [[
biconnected_components[idx], biconnected_edges[idx]
] for idx in range(len(biconnected_components))]
return components_and_edges
def complex_triangle_check(graph):
for compedges in nx.biconnected_component_edges(graph):
comp = nx.Graph()
comp.add_edges_from(compedges)
# print("hi")
# print(comp.edges)
H = comp.to_directed()
# H = G.copy()
# Get all triangles
all_cycles = list(nx.simple_cycles(H))
all_triangles = []
for cycle in all_cycles:
if len(cycle) == 3:
all_triangles.append(cycle)
# Get edges on outer boundary
# print(f"all triangles {all_triangles}")
outer_boundary = []
for edge in H.edges:
count = 0
for triangle in all_triangles:
if edge[0] in triangle and edge[1] in triangle:
count += 1
if count == 2:
outer_boundary.append(edge)
# Get Vertex-Set of outerboundary
outer_vertices = []
for edge in outer_boundary:
if edge[0] not in outer_vertices:
outer_vertices.append(edge[0])
if edge[1] not in outer_vertices:
outer_vertices.append(edge[1])
# print(f"outer vertices {outer_vertices}")
if all_triangles:
if 2 * len(comp) - 5 + 3 - len(
outer_vertices) - len(all_triangles) / 2:
# print("complex")
# print(2*len(comp)-5+3-len(outer_vertices)-len(all_triangles))
# print(2*len(comp))
# print(len(outer_vertices))
# print(len(all_triangles))
return False
return True
def test_biconnected_components1():
# graph example from
# https://web.archive.org/web/20121229123447/http://www.ibluemojo.com/school/articul_algorithm.html
edges = [
(0, 1),
(0, 5),
(0, 6),
(0, 14),
(1, 5),
(1, 6),
(1, 14),
(2, 4),
(2, 10),
(3, 4),
(3, 15),
(4, 6),
(4, 7),
(4, 10),
(5, 14),
(6, 14),
(7, 9),
(8, 9),
(8, 12),
(8, 13),
(10, 15),
(11, 12),
(11, 13),
(12, 13),
]
G = nx.Graph(edges)
pts = set(nx.articulation_points(G))
assert pts == {4, 6, 7, 8, 9}
comps = list(nx.biconnected_component_edges(G))
answer = [
[(3, 4), (15, 3), (10, 15), (10, 4), (2, 10), (4, 2)],
[(13, 12), (13, 8), (11, 13), (12, 11), (8, 12)],
[(9, 8)],
[(7, 9)],
[(4, 7)],
[(6, 4)],
[(14, 0), (5, 1), (5, 0), (14, 5), (14, 1), (6, 14), (6, 0), (1, 6),
(0, 1)],
]
assert_components_edges_equal(comps, answer)
def test_biconnected_components1():
# graph example from
# http://www.ibluemojo.com/school/articul_algorithm.html
edges=[
(0, 1), (0, 5), (0, 6), (0, 14), (1, 5), (1, 6), (1, 14), (2, 4),
(2, 10), (3, 4), (3, 15), (4, 6), (4, 7), (4, 10), (5, 14), (6, 14),
(7, 9), (8, 9), (8, 12), (8, 13), (10, 15), (11, 12), (11, 13), (12, 13)
]
G=nx.Graph(edges)
pts = set(nx.articulation_points(G))
assert_equal(pts, {4, 6, 7, 8, 9})
comps = list(nx.biconnected_component_edges(G))
answer = [
[(3, 4), (15, 3), (10, 15), (10, 4), (2, 10), (4, 2)],
[(13, 12), (13, 8), (11, 13), (12, 11), (8, 12)],
[(9, 8)],
[(7, 9)],
[(4, 7)],
[(6, 4)],
[(14, 0), (5, 1), (5, 0), (14, 5), (14, 1), (6, 14), (6, 0), (1, 6), (0, 1)],
]
assert_components_edges_equal(comps, answer)
def test_biconnected_components2():
G = nx.Graph()
nx.add_cycle(G, "ABC")
nx.add_cycle(G, "CDE")
nx.add_cycle(G, "FIJHG")
nx.add_cycle(G, "GIJ")
G.add_edge("E", "G")
comps = list(nx.biconnected_component_edges(G))
answer = [
[
tuple("GF"),
tuple("FI"),
tuple("IG"),
tuple("IJ"),
tuple("JG"),
tuple("JH"),
tuple("HG"),
],
[tuple("EG")],
[tuple("CD"), tuple("DE"), tuple("CE")],
[tuple("AB"), tuple("BC"), tuple("AC")],
]
assert_components_edges_equal(comps, answer)
def component_break(given_graph):
"""
Given a graph,
returns [list of the 2 outer components(1 articulation point) with 2cip],
[list of other inner components(2 articulation points) with 0 cip]
"""
test_graph = given_graph.copy()
cutvertices = list(nx.articulation_points(test_graph))
# O(biconnected_components * cutvertices)
inner_components = []
outer_components = []
if len(cutvertices) == 0:
single_component = test_graph
return 0, 0, single_component
for peice_edges in nx.biconnected_component_edges(test_graph):
# Find num cutvertices
# num_cutverts = nx.intersection(peice, cutvertices)
peice = nx.Graph()
peice.add_edges_from(list(peice_edges))
num_cutverts = 0
for cutvert in cutvertices:
if cutvert in peice.nodes():
num_cutverts += 1
if num_cutverts == 2:
inner_components.append(peice)
elif num_cutverts == 1:
outer_components.append(peice)
else:
print("Illegal Case 1")
print(test_graph.edges())
if len(outer_components) > 2:
print("Illegal Case 2")
print(test_graph)
return outer_components, inner_components, 0
# colors_to_select.remove(color)
# colors_of_edges.append((color))
# nodes_color_alpha.append(0.4)
# edges_color_alpha.append(0.6)
# edge_width_l.append(4.0)
# print str(" ")
# Gcc=sorted(nx.biconnected_connected_component_subgraphs(G), key = len, reverse=True)
# Ggc=Gcc[0]
# graph='Ggc'
# print 'Nodes of giant connected component', graph+':', Ggc.nodes()
# print 'Edges of giant connected component', graph+':', Ggc.edges()
# print str(" ")
print 'The biconnected component edges of G are:', list(
nx.biconnected_component_edges(G))
print str(" ")
print 'The articulation points of G are:', set(nx.articulation_points(G))
print str(" ")
print 'Isolated nodes:', nx.isolates(G)
print str(" ")
# n1=list(set(G.nodes()) - set(Ggc.nodes()) - set(nx.isolates(G)))
# print 'Non-isolated nodes outside the giant connected component:', n1
# N1=G.subgraph(n1)
# print 'Edges among non-isolated nodes outside the giant connected component:', N1.edges()
plt.figure()
def find_max_biconnected_component(G):
gr = maximum_connected_component(G)
bnodes = nx.biconnected_component_edges(gr)
return list(bnodes).pop()
def test_null_graph():
G = nx.Graph()
assert not nx.is_biconnected(G)
assert list(nx.biconnected_components(G)) == []
assert list(nx.biconnected_component_edges(G)) == []
assert list(nx.articulation_points(G)) == []
def biconnected_components_gen(new_graph):
return [
edge for list in nx.biconnected_component_edges(new_graph)
for edge in list
]
# color=random.choice(colors_to_select)
# colors_to_select.remove(color)
# colors_of_edges.append((color))
# nodes_color_alpha.append(0.4)
# edges_color_alpha.append(0.6)
# edge_width_l.append(4.0)
# print str(" ")
# Gcc=sorted(nx.biconnected_connected_component_subgraphs(G), key = len, reverse=True)
# Ggc=Gcc[0]
# graph='Ggc'
# print 'Nodes of giant connected component', graph+':', Ggc.nodes()
# print 'Edges of giant connected component', graph+':', Ggc.edges()
# print str(" ")
print 'The biconnected component edges of G are:', list(nx.biconnected_component_edges(G))
print str(" ")
print 'The articulation points of G are:', set(nx.articulation_points(G))
print str(" ")
print 'Isolated nodes:', nx.isolates(G)
print str(" ")
# n1=list(set(G.nodes()) - set(Ggc.nodes()) - set(nx.isolates(G)))
# print 'Non-isolated nodes outside the giant connected component:', n1
# N1=G.subgraph(n1)
# print 'Edges among non-isolated nodes outside the giant connected component:', N1.edges()
def test_null_graph():
G = nx.Graph()
assert_false(nx.is_biconnected(G))
assert_equal(list(nx.biconnected_components(G)), [])
assert_equal(list(nx.biconnected_component_edges(G)), [])
assert_equal(list(nx.articulation_points(G)), [])
def test_null_graph():
G = nx.Graph()
assert_false(nx.is_biconnected(G))
assert_equal(list(nx.biconnected_components(G)), [])
assert_equal(list(nx.biconnected_component_edges(G)), [])
assert_equal(list(nx.articulation_points(G)), [])
def label_edges(self, dungeon):
biconnected_component_edges = nx.biconnected_component_edges(dungeon)
for edge, edge_data in dungeon.edges(data=True):
if edge in biconnected_component_edges:
edge_data['important'] = True
