Abstract
This paper considers the spectral determinant of quantum graph families with chaotic classical limit. 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 for graphs without symmetries. 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. Related results for graphs with time-reversal symmetry are given.