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1"""Semiconnectedness."""
3import networkx as nx
4from networkx.utils import not_implemented_for, pairwise
6__all__ = ["is_semiconnected"]
9@not_implemented_for("undirected")
10@nx._dispatchable
11def is_semiconnected(G):
12 r"""Returns True if the graph is semiconnected, False otherwise.
14 A graph is semiconnected if and only if for any pair of nodes, either one
15 is reachable from the other, or they are mutually reachable.
17 This function uses a theorem that states that a DAG is semiconnected
18 if for any topological sort, for node $v_n$ in that sort, there is an
19 edge $(v_i, v_{i+1})$. That allows us to check if a non-DAG `G` is
20 semiconnected by condensing the graph: i.e. constructing a new graph `H`
21 with nodes being the strongly connected components of `G`, and edges
22 (scc_1, scc_2) if there is a edge $(v_1, v_2)$ in `G` for some
23 $v_1 \in scc_1$ and $v_2 \in scc_2$. That results in a DAG, so we compute
24 the topological sort of `H` and check if for every $n$ there is an edge
25 $(scc_n, scc_{n+1})$.
27 Parameters
28 ----------
29 G : NetworkX graph
30 A directed graph.
32 Returns
33 -------
34 semiconnected : bool
35 True if the graph is semiconnected, False otherwise.
37 Raises
38 ------
39 NetworkXNotImplemented
40 If the input graph is undirected.
42 NetworkXPointlessConcept
43 If the graph is empty.
45 Examples
46 --------
47 >>> G = nx.path_graph(4, create_using=nx.DiGraph())
48 >>> print(nx.is_semiconnected(G))
49 True
50 >>> G = nx.DiGraph([(1, 2), (3, 2)])
51 >>> print(nx.is_semiconnected(G))
52 False
54 See Also
55 --------
56 is_strongly_connected
57 is_weakly_connected
58 is_connected
59 is_biconnected
60 """
61 if len(G) == 0:
62 raise nx.NetworkXPointlessConcept(
63 "Connectivity is undefined for the null graph."
64 )
66 if not nx.is_weakly_connected(G):
67 return False
69 H = nx.condensation(G)
71 return all(H.has_edge(u, v) for u, v in pairwise(nx.topological_sort(H)))