venv/lib/python3.10/site-packages/networkx/algorithms/components/semiconnected.py

"""Semiconnectedness."""

import networkx as nx
from networkx.utils import not_implemented_for, pairwise

__all__ = ["is_semiconnected"]


@not_implemented_for("undirected")
@nx._dispatchable
def is_semiconnected(G):
    r"""Returns True if the graph is semiconnected, False otherwise.

    A graph is semiconnected if and only if for any pair of nodes, either one
    is reachable from the other, or they are mutually reachable.

    This function uses a theorem that states that a DAG is semiconnected
    if for any topological sort, for node $v_n$ in that sort, there is an
    edge $(v_i, v_{i+1})$. That allows us to check if a non-DAG `G` is
    semiconnected by condensing the graph: i.e. constructing a new graph `H`
    with nodes being the strongly connected components of `G`, and edges
    (scc_1, scc_2) if there is a edge $(v_1, v_2)$ in `G` for some
    $v_1 \in scc_1$ and $v_2 \in scc_2$. That results in a DAG, so we compute
    the topological sort of `H` and check if for every $n$ there is an edge
    $(scc_n, scc_{n+1})$.

    Parameters
    ----------
    G : NetworkX graph
        A directed graph.

    Returns
    -------
    semiconnected : bool
        True if the graph is semiconnected, False otherwise.

    Raises
    ------
    NetworkXNotImplemented
        If the input graph is undirected.

    NetworkXPointlessConcept
        If the graph is empty.

    Examples
    --------
    >>> G = nx.path_graph(4, create_using=nx.DiGraph())
    >>> print(nx.is_semiconnected(G))
    True
    >>> G = nx.DiGraph([(1, 2), (3, 2)])
    >>> print(nx.is_semiconnected(G))
    False

    See Also
    --------
    is_strongly_connected
    is_weakly_connected
    is_connected
    is_biconnected
    """
    if len(G) == 0:
        raise nx.NetworkXPointlessConcept(
            "Connectivity is undefined for the null graph."
        )

    if not nx.is_weakly_connected(G):
        return False

    H = nx.condensation(G)

    return all(H.has_edge(u, v) for u, v in pairwise(nx.topological_sort(H)))