Generalized Paley graphs have real spectra exactly when undirected; directed versions with three eigenvalues are only oriented Paley graphs or their unions; weak Waring numbers reduce to classical Waring numbers over finite fields.
Parameters of directed strongly regular graphs, http://homepages.cwi.nl/ aeb/math/dsrg/dsrg.html
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The nature of the spectrum of generalized Paley graphs and weak Waring numbers over finite fields
Generalized Paley graphs have real spectra exactly when undirected; directed versions with three eigenvalues are only oriented Paley graphs or their unions; weak Waring numbers reduce to classical Waring numbers over finite fields.