  We characterize all graphs for which there are eigenvectors of the graph
Laplacian having all their components in {-1,+1} or {-1,0,+ 1}. Graphs having
eigenvectors with components in {-1,+1} are called bivalent and are shown to be
the regular bipartite graphs and their extensions obtained by adding edges
between vertices with the same value for the given eigenvector. Graphs with
eigenvectors with components in {-1,0,+ 1} are called trivalent and are shown
to be soft-regular graphs -graphs such that vertices associated with non-zero
components have the same degree- and their extensions via some transformations.
