The nodal domains of eigenvectors of the discrete Schrodinger operator on
simple, finite and connected graphs are considered. Courant's well known nodal
domain theorem applies in the present case, and sets an upper bound to the
number of nodal domains of eigenvectors: Arranging the spectrum as a non
decreasing sequence, and denoting by $\nu_n$ the number of nodal domains of the
$n$'th eigenvector, Courant's theorem guarantees that the nodal deficiency
$n-\nu_n$ is non negative. (The above applies for generic eigenvectors.