  The paper considers the spectral determinant of quantum graph families with
chaotic classical limit and no symmetries. The secular coefficients of the
spectral determinant are found to follow distributions with zero mean and
variance approaching a constant in the limit of large network size. This
constant is in general different from the random matrix result and depends on
the classical limit. A closed expression for this system dependent constant is
given here explicitly in terms of the spectrum of an underlying Markov process.
