  It is well known that, in general, part of the spectrum of a graph can be
obtained from the adjacency matrix of its quotient graph given by a regular
partition. In this paper, we propose a method to obtain all the spectrum, and
also the local spectra, of a graph $\Gamma$ from the quotient matrices of some
of its regular partitions. As examples, it is shown how to find the eigenvalues
and (local) multiplicities of walk-regular, distance-regular, and
distance-biregular graphs.
