68 lines
1.8 KiB
Python
68 lines
1.8 KiB
Python
r"""Generators for cographs
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A cograph is a graph containing no path on four vertices.
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Cographs or $P_4$-free graphs can be obtained from a single vertex
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by disjoint union and complementation operations.
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References
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----------
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.. [0] D.G. Corneil, H. Lerchs, L.Stewart Burlingham,
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"Complement reducible graphs",
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Discrete Applied Mathematics, Volume 3, Issue 3, 1981, Pages 163-174,
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ISSN 0166-218X.
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"""
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import networkx as nx
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from networkx.utils import py_random_state
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__all__ = ["random_cograph"]
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@py_random_state(1)
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@nx._dispatch(graphs=None)
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def random_cograph(n, seed=None):
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r"""Returns a random cograph with $2 ^ n$ nodes.
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A cograph is a graph containing no path on four vertices.
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Cographs or $P_4$-free graphs can be obtained from a single vertex
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by disjoint union and complementation operations.
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This generator starts off from a single vertex and performs disjoint
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union and full join operations on itself.
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The decision on which operation will take place is random.
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Parameters
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----------
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n : int
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The order of the cograph.
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seed : integer, random_state, or None (default)
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Indicator of random number generation state.
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See :ref:`Randomness<randomness>`.
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Returns
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-------
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G : A random graph containing no path on four vertices.
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See Also
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--------
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full_join
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union
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References
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----------
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.. [1] D.G. Corneil, H. Lerchs, L.Stewart Burlingham,
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"Complement reducible graphs",
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Discrete Applied Mathematics, Volume 3, Issue 3, 1981, Pages 163-174,
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ISSN 0166-218X.
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"""
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R = nx.empty_graph(1)
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for i in range(n):
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RR = nx.relabel_nodes(R.copy(), lambda x: x + len(R))
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if seed.randint(0, 1) == 0:
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R = nx.full_join(R, RR)
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else:
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R = nx.disjoint_union(R, RR)
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return R
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