  In this paper we define the (edge-weighted) Cayley graph associated to a
generalized Boolean function, introduce a notion of strong regularity and give
several of its properties. We show some connections between this concept and
generalized bent functions (gbent), that is, functions with flat Walsh-Hadamard
spectrum. In particular, we find a complete characterization of quartic gbent
functions in terms of the strong regularity of their associated Cayley graph.
