Path

A path joining two vertices $P_i$ and $P_j$ in a given digraph is a sequence of distinct points (vertices) $P_i, P_{a_1}, P_{a_2}, \dots, P_{a_r}, P_j$ and directed edges $P_i \rightarrow P_{a_1} , P_{a_1} \rightarrow P_{a_2}, \cdots, P_{a_{r-1}} \rightarrow P_{a_r}$ and $\ P_{a_r} \rightarrow P_j$

Example: In the following digraph there more than one path from $P_1$ to $P_3$. One of them consists of only three points $P_1, P_2, P_3$. A different path from $P_1$ to $P_3$ consists of the points $P_1, P_2, P_4, p_5$ and $P_3$.

Figure 5

The path which contains the points $P_1, P_2, P_3, P_4$ and $P_5$ with edges $P_1 \rightarrow P_2$, $P_2 \rightarrow P_4$, $P_4 \rightarrow P_5 \rightarrow P_3$ connects $P_1$ to $P_3$.

Figure 6

Also $P_1, P_2, P_3$ with edges $P_1 \rightarrow P_2$ and $P_2 \rightarrow P_3$ is path from $P_1$ to $P_3$. which is represented in the following figure:

Figure 7