# Connected Digraphs

**CONNECTED DIGRAPHS**

**Strongly Connected**: A digraph G is said to be strongly connected if there is atleast one directed path from every vertex to every other vertex.

**Weakly Connected**: A digraph G is said to be weakly connected if its corresponding undirected graph is connected

but G is not strongly connected.

Fig. 8.6, one of the digraphs is strongly connected, and the other one is weakly connected.

**Component and Fragments**: Each maximal connected (weakly or strongly) subgraph of a digraph G is called a component of G. But within each component of G the maximal strongly connected subgraphs are called the fragments (or strongly connected fragments) of G.

**For example,** the digraph in Fig. 10, consists of two components. The component g1 contains three fragments {e1, e2}, {e5, e6, e7, e8} and {e10}.

We observe that e3, e4 and e9 do not appear in any fragment of g1.