Random quantum graphs

We prove a number of results to the effect that generic quantum graphs (defined via operator systems as in work Duan-Severini-Winter / Weaver) have few symmetries: for Zariski-dense open set tuples $(X_1,\cdots,X_d)$ traceless self-adjoint operators $n\times n$ matrix algebra corresponding system has trivial automorphism group, largest possible range parameters: $2\le d\le n^2-3$. Moreover, group is generically abelian larger parameter $1\le n^2-2$. This then implies those respective parameters random-quantum-graph model built on GUE ensembles $X_i$'s (mimicking Erd\H{o}s-R\'{e}nyi $G(n,p)$ model) trivial/abelian almost surely.