# Revision history [back]

### Why a graph with one vertex and no edge considered strongly connected?

Everytime I need to use the strongly connected components of a graph in Sage, I am looking for a graph where there exists a biinfinite path going trough all the vertices of a components infinitely often. In that sense, I dislike the behavior of the methods is_strongly_connected and strongly_connected_components.

More precisely, I agree with this:

sage: G = DiGraph(loops=True)
sage: G.is_strongly_connected()
True


I dislike that this is not returning False:

sage: G = DiGraph()
sage: G.is_strongly_connected()
True


and I dislike that strongly_connected_components method and its friends always return a lot of garbage components containing one vertex with no loops where no biinfinite path can live in:

sage: G = DiGraph()
sage: G.add_edges([(i,i+1) for i in range(9)])
sage: G.strongly_connected_components()
[[6, 7, 8, 9], [5], [4], [3], [2], [1], [0]]
sage: G.strongly_connected_components_subgraphs()
[Subgraph of (): Digraph on 4 vertices,
Subgraph of (): Digraph on 1 vertex,
Subgraph of (): Digraph on 1 vertex,
Subgraph of (): Digraph on 1 vertex,
Subgraph of (): Digraph on 1 vertex,
Subgraph of (): Digraph on 1 vertex,
Subgraph of (): Digraph on 1 vertex]


Do you think like me that the definition should be changed to :

sage: [sub for sub in G.strongly_connected_components_subgraphs() if sub.num_edges()]
[Subgraph of (): Digraph on 4 vertices]


?