If I am given the adjacency matrix
<br />
\left[ {\begin{array}{ccccc}<br />
0 & 1 & 0 & 0 & 0 \\<br />
0 & 0 & 1 & 0 & 0 \\<br />
1 & 0 & 0 & 0 & 0 \\<br />
0 & 0 & 1 & 1 & 0 \\<br />
\end{array} } \right]<br />
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?