Characteristic power series of graph limits

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