# 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.add_edge((0,0))
sage: G.is_strongly_connected()
True
```

I dislike that this is not returning False:

```
sage: G = DiGraph()
sage: G.add_vertex(0)
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.add_edge(9,6)
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]
```

?