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?