  Using periodic-orbit theory beyond the diagonal approximation we investigate
the form factor, $K(\tau)$, of a generic quantum graph with mixing classical
dynamics and time-reversal symmetry. We calculate the contribution from pairs
of self-intersecting orbits that differ from each other only in the orientation
of a single loop. In the limit of large graphs, these pairs produce a
contribution $-2\tau^2$ to the form factor which agrees with random-matrix
theory.
