is_semiconnected#

is_semiconnected(G)[source]#

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 $v_1\in sc{c}_1$ and $v_2\in sc{c}_2$. That results in a DAG, so we compute the topological sort of H and check if for every $n$ there is an edge $(sc{c}_n,sc{c}_{n+1})$.

Parameters:

GNetworkX graph

A directed graph.

Returns:

semiconnectedbool

True if the graph is semiconnected, False otherwise.

Raises:

NetworkXNotImplemented

If the input graph is undirected.

NetworkXPointlessConcept

If the graph is empty.

See also

is_strongly_connected

is_weakly_connected

is_connected

is_biconnected

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