def test_full_join_graph():
# Simple Graphs
G = nx.Graph()
G.add_node(0)
G.add_edge(1, 2)
H = nx.Graph()
H.add_edge(3, 4)
U = nx.full_join(G, H)
assert_equal(set(U), set(G) | set(H))
assert_equal(len(U), len(G) + len(H))
assert_equal(len(U.edges()),
len(G.edges()) + len(H.edges()) + len(G) * len(H))
# Rename
U = nx.full_join(G, H, rename=('g', 'h'))
assert_equal(set(U), set(['g0', 'g1', 'g2', 'h3', 'h4']))
assert_equal(len(U), len(G) + len(H))
assert_equal(len(U.edges()),
len(G.edges()) + len(H.edges()) + len(G) * len(H))
# Rename graphs with string-like nodes
G = nx.Graph()
G.add_node("a")
G.add_edge("b", "c")
H = nx.Graph()
H.add_edge("d", "e")
U = nx.full_join(G, H, rename=('g', 'h'))
assert_equal(set(U), set(['ga', 'gb', 'gc', 'hd', 'he']))
assert_equal(len(U), len(G) + len(H))
assert_equal(len(U.edges()),
len(G.edges()) + len(H.edges()) + len(G) * len(H))
# DiGraphs
G = nx.DiGraph()
G.add_node(0)
G.add_edge(1, 2)
H = nx.DiGraph()
H.add_edge(3, 4)
U = nx.full_join(G, H)
assert_equal(set(U), set(G) | set(H))
assert_equal(len(U), len(G) + len(H))
assert_equal(len(U.edges()),
len(G.edges()) + len(H.edges()) + len(G) * len(H) * 2)
# DiGraphs Rename
U = nx.full_join(G, H, rename=('g', 'h'))
assert_equal(set(U), set(['g0', 'g1', 'g2', 'h3', 'h4']))
assert_equal(len(U), len(G) + len(H))
assert_equal(len(U.edges()),
len(G.edges()) + len(H.edges()) + len(G) * len(H) * 2)
def test_full_join_graph():
# Simple Graphs
G = nx.Graph()
G.add_node(0)
G.add_edge(1, 2)
H = nx.Graph()
H.add_edge(3, 4)
U = nx.full_join(G, H)
assert set(U) == set(G) | set(H)
assert len(U) == len(G) + len(H)
assert len(U.edges()) == len(G.edges()) + len(H.edges()) + len(G) * len(H)
# Rename
U = nx.full_join(G, H, rename=("g", "h"))
assert set(U) == {"g0", "g1", "g2", "h3", "h4"}
assert len(U) == len(G) + len(H)
assert len(U.edges()) == len(G.edges()) + len(H.edges()) + len(G) * len(H)
# Rename graphs with string-like nodes
G = nx.Graph()
G.add_node("a")
G.add_edge("b", "c")
H = nx.Graph()
H.add_edge("d", "e")
U = nx.full_join(G, H, rename=("g", "h"))
assert set(U) == {"ga", "gb", "gc", "hd", "he"}
assert len(U) == len(G) + len(H)
assert len(U.edges()) == len(G.edges()) + len(H.edges()) + len(G) * len(H)
# DiGraphs
G = nx.DiGraph()
G.add_node(0)
G.add_edge(1, 2)
H = nx.DiGraph()
H.add_edge(3, 4)
U = nx.full_join(G, H)
assert set(U) == set(G) | set(H)
assert len(U) == len(G) + len(H)
assert len(
U.edges()) == len(G.edges()) + len(H.edges()) + len(G) * len(H) * 2
# DiGraphs Rename
U = nx.full_join(G, H, rename=("g", "h"))
assert set(U) == {"g0", "g1", "g2", "h3", "h4"}
assert len(U) == len(G) + len(H)
assert len(
U.edges()) == len(G.edges()) + len(H.edges()) + len(G) * len(H) * 2
def test_full_join_multigraph():
# MultiGraphs
G = nx.MultiGraph()
G.add_node(0)
G.add_edge(1, 2)
H = nx.MultiGraph()
H.add_edge(3, 4)
U = nx.full_join(G, H)
assert_equal(set(U), set(G) | set(H))
assert_equal(len(U), len(G) + len(H))
assert_equal(len(U.edges()),
len(G.edges()) + len(H.edges()) + len(G) * len(H))
# MultiGraphs rename
U = nx.full_join(G, H, rename=('g', 'h'))
assert_equal(set(U), set(['g0', 'g1', 'g2', 'h3', 'h4']))
assert_equal(len(U), len(G) + len(H))
assert_equal(len(U.edges()),
len(G.edges()) + len(H.edges()) + len(G) * len(H))
# MultiDiGraphs
G = nx.MultiDiGraph()
G.add_node(0)
G.add_edge(1, 2)
H = nx.MultiDiGraph()
H.add_edge(3, 4)
U = nx.full_join(G, H)
assert_equal(set(U), set(G) | set(H))
assert_equal(len(U), len(G) + len(H))
assert_equal(len(U.edges()),
len(G.edges()) + len(H.edges()) + len(G) * len(H) * 2)
# MultiDiGraphs rename
U = nx.full_join(G, H, rename=('g', 'h'))
assert_equal(set(U), set(['g0', 'g1', 'g2', 'h3', 'h4']))
assert_equal(len(U), len(G) + len(H))
assert_equal(len(U.edges()),
len(G.edges()) + len(H.edges()) + len(G) * len(H) * 2)
def test_full_join_multigraph():
# MultiGraphs
G = nx.MultiGraph()
G.add_node(0)
G.add_edge(1, 2)
H = nx.MultiGraph()
H.add_edge(3, 4)
U = nx.full_join(G, H)
assert set(U) == set(G) | set(H)
assert len(U) == len(G) + len(H)
assert len(U.edges()) == len(G.edges()) + len(H.edges()) + len(G) * len(H)
# MultiGraphs rename
U = nx.full_join(G, H, rename=("g", "h"))
assert set(U) == {"g0", "g1", "g2", "h3", "h4"}
assert len(U) == len(G) + len(H)
assert len(U.edges()) == len(G.edges()) + len(H.edges()) + len(G) * len(H)
# MultiDiGraphs
G = nx.MultiDiGraph()
G.add_node(0)
G.add_edge(1, 2)
H = nx.MultiDiGraph()
H.add_edge(3, 4)
U = nx.full_join(G, H)
assert set(U) == set(G) | set(H)
assert len(U) == len(G) + len(H)
assert len(
U.edges()) == len(G.edges()) + len(H.edges()) + len(G) * len(H) * 2
# MultiDiGraphs rename
U = nx.full_join(G, H, rename=("g", "h"))
assert set(U) == {"g0", "g1", "g2", "h3", "h4"}
assert len(U) == len(G) + len(H)
assert len(
U.edges()) == len(G.edges()) + len(H.edges()) + len(G) * len(H) * 2
def random_cograph(n, seed=None):
r"""Returns a random cograph with $2 ^ n$ nodes.
A cograph is a graph containing no path on four vertices.
Cographs or $P_4$-free graphs can be obtained from a single vertex
by disjoint union and complementation operations.
This generator starts off from a single vertex and performes disjoint
union and full join operations on itself.
The decision on which operation will take place is random.
Parameters
----------
n : int
The order of the cograph.
seed : integer, random_state, or None (default)
Indicator of random number generation state.
See :ref:`Randomness<randomness>`.
Returns
-------
G : A random graph containing no path on four vertices.
See Also
--------
full_join
union
References
----------
.. [1] D.G. Corneil, H. Lerchs, L.Stewart Burlingham,
"Complement reducible graphs",
Discrete Applied Mathematics, Volume 3, Issue 3, 1981, Pages 163-174,
ISSN 0166-218X.
"""
R = nx.empty_graph(1)
for i in range(n):
RR = nx.relabel_nodes(R.copy(), lambda x: x + len(R))
if seed.randint(0, 1) == 0:
R = nx.full_join(R, RR)
else:
R = nx.disjoint_union(R, RR)
return R
