Source code for networkx.algorithms.components.semiconnected

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

__all__ = ["is_semiconnected"]

[docs] @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)))