Directed Graph

A directed graph or digraph is a finite set of vertices together with a finite set of directed edges.

Example :

Figure3

In this Example $P_1, P_2, P_3$ are vertices, and $(P_1, P_3)$ and $(P_3, P_2)$ are directed edges. We show directed edges as $(P_1, P_3)$ or $P_1 \rightarrow P_3$ which means "$P_1$ is connected to $P_3$."

Two oppositely pointing arrow on the graph connecting $P_i$ to $P_j$ and $P_j$ to $P_i$ will be represented as $P_i \leftrightarrow P_j$ which implies that both $P_i \rightarrow P_j$ and $P_j \rightarrow P_i$ hold.

Figure 4

In this example the vertices are $P_1, P_2, P_3$, and edges are $\underbrace{(P_1, P_2), (P_2, P_1)}_{P_1 \leftrightarrow P_2}$, $\underbrace{(P_3, P_2)}_{P_3 \rightarrow P_2}$, $\underbrace{(P_1, P_3)}_{P_1 \rightarrow P_3}$.