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In a series of two papers we investigate the universal spectral statistics ofchaotic quantum systems in the ten known symmetry classes of quantum mechanics.In this first paper we focus on the construction of appropriate ensembles ofstar graphs in the ten symmetry classes. A generalization of theBohigas-Giannoni-Schmit conjecture is given that covers all these symmetryclasses. The conjecture is supported by numerical results that demonstrate thefidelity of the spectral statistics of star graphs to the correspondingGaussian random-matrix theories.Comment: 15 page

Universal spectral statistics in Wigner-Dyson, chiral, and Andreev star graphs. I. Construction and numerical results