If I am given the adjacency matrix
$\displaystyle
\left[ {\begin{array}{ccccc}
0 & 1 & 0 & 0 & 0 \\
0 & 0 & 1 & 0 & 0 \\
1 & 0 & 0 & 0 & 0 \\
0 & 0 & 1 & 1 & 0 \\
\end{array} } \right]
$
then how do I find the number of vertices to determine if it's strongly connected?

I guess this example could easily be graphed, but for a more complex scenario what would be a rigorous method?