Robert - good, you see the problem.

You might try counting the paths of various lengths in this graph:

and compare it to taking powers of this matrix:

\[ \left( \begin{array}{cc} 1 & 1 \\\ 1 & 0 \end{array} \right) .\]

You might try counting the paths of various lengths in this graph:

and compare it to taking powers of this matrix:

\[ \left( \begin{array}{cc} 1 & 1 \\\ 1 & 0 \end{array} \right) .\]