Given a directed graph, we need to find the number of paths with exactly **k** edges from source **u** to the destination **v**.
We use `adjacency matrix`

of the given graph in which value of `adj[i][j]`

represents if there is an edge from vertex `i`

to vertex `j`

in the graph. If the value is `1`

then there is an edge from vertex `i`

to vertex `j`

else, if value is `0`

then there is no edges from vertex `i`

to vertex `j`

in the graph.
To understand the problem let's take an example of a graph with 6 vertices {0, 1, 2, 3, 4, 5} and edges. Now let's find number of paths from vertex `0`

to vertex `2`

with 2 edges. Below a diagram of the graph is given:

This is a companion discussion topic for the original entry at http://iq.opengenus.org/number-of-paths-with-k-edges/