72 lines
2 KiB
Python
72 lines
2 KiB
Python
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"""Semiconnectedness."""
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import networkx as nx
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from networkx.utils import not_implemented_for, pairwise
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__all__ = ["is_semiconnected"]
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@not_implemented_for("undirected")
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@nx._dispatchable
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def is_semiconnected(G):
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r"""Returns True if the graph is semiconnected, False otherwise.
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A graph is semiconnected if and only if for any pair of nodes, either one
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is reachable from the other, or they are mutually reachable.
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This function uses a theorem that states that a DAG is semiconnected
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if for any topological sort, for node $v_n$ in that sort, there is an
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edge $(v_i, v_{i+1})$. That allows us to check if a non-DAG `G` is
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semiconnected by condensing the graph: i.e. constructing a new graph `H`
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with nodes being the strongly connected components of `G`, and edges
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(scc_1, scc_2) if there is a edge $(v_1, v_2)$ in `G` for some
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$v_1 \in scc_1$ and $v_2 \in scc_2$. That results in a DAG, so we compute
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the topological sort of `H` and check if for every $n$ there is an edge
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$(scc_n, scc_{n+1})$.
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Parameters
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----------
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G : NetworkX graph
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A directed graph.
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Returns
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-------
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semiconnected : bool
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True if the graph is semiconnected, False otherwise.
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Raises
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------
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NetworkXNotImplemented
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If the input graph is undirected.
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NetworkXPointlessConcept
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If the graph is empty.
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Examples
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--------
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>>> G = nx.path_graph(4, create_using=nx.DiGraph())
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>>> print(nx.is_semiconnected(G))
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True
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>>> G = nx.DiGraph([(1, 2), (3, 2)])
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>>> print(nx.is_semiconnected(G))
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False
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See Also
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--------
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is_strongly_connected
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is_weakly_connected
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is_connected
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is_biconnected
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"""
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if len(G) == 0:
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raise nx.NetworkXPointlessConcept(
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"Connectivity is undefined for the null graph."
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)
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if not nx.is_weakly_connected(G):
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return False
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H = nx.condensation(G)
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return all(H.has_edge(u, v) for u, v in pairwise(nx.topological_sort(H)))
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