what is the difference between directed edges and paths? I understand that both are made by connecting nodes and both have a direction in the sense that P_1 --> P_2 is differnt than P_2-->P_1
In my opinion, by a path is meant a sequence of vertices such that from each of its vertices where is an edge to the next vertex in the sequence. The length of a path is the number of the edges that the path uses. If the length is equal to 1, the path is exact the edge.