Adjacency Matrix of Complete Graph with 4 vertices A = $\begin{bmatrix} 0 & 1& 1& 1\\ 1& 0& 1& 1\\ 1& 1& 0& 1\\ 1& 1& 1& 0 \end{bmatrix}$
The number of paths of length five from ith vertex to jth vertex is the (i, j)th entry of A5.
After Calculation A5 = $\begin{bmatrix} 60 & 61& 61& 61\\ 61& 60 & 61& 61\\ 61& 61& 60& 61\\ 61& 61& 61& 60 \end{bmatrix}$
Total number of paths of length five from ith vertex to jth vertex such that (i$\neq$j)= 61