Let \(D(V,E,\alpha,\omega)\) be a non-empty digraph.
\(D\) is called disconnected, if for some vertices \(x,y\in V\) there is either a path in \(D\) from \(x\) to \(y\) nor a path from \(y\) to \(x\).
\(D\) is called weakly connected, if for any two vertices \(x,y\in V\) there is a path in \(D\) from \(x\) to \(y\) or from \(y\) to \(x\).
\(D\) is called strongly connected, if for any two vertices \(x,y\in V\) there is a path in \(D\) from \(x\) to \(y\) and from \(y\) to \(x\).
In the digraph above, there is no path to or from \(f\). Thus the digraph is disconnected.
However, the subgraph \(D[a,b,c,d,e]\) is weakly connected, since \(ade\) is a path from \(a\) to \(e\), but there is no path from \(e\) to \(a\).
The subgraph \(D[a,b,c]\) is strongly connected, since for any pairs of vertices \(a,b\), and \(b,c\) and \(c,a\), there are paths in both directions.
