Characteristic Power Series of Graph Limits

Joshua N. Cooper

In this note, we show how to obtain a ``characteristic power series'' of graphons -- infinite limits of graphs -- as the limit of normalized reciprocal characteristic polynomials. This leads to a characterization of graph quasi-randomness and another perspective on spectral theory for graphons, including a complete description of the function in terms of the spectrum of the graphon as a self-adjoint kernel operator.

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