  In this note, we show how to obtain a "characteristic power series" of
graphons -- infinite limits of dense graphs -- as the limit of normalized
reciprocal characteristic polynomials. This leads to a new characterization of
graph quasi-randomness and another perspective on spectral theory for graphons,
a complete description of the function in terms of the spectrum of the graphon
as a self-adjoint kernel operator. Interestingly, while we apply a standard
regularization to classical determinants, it is unclear how necessary this is.
