  This note discusses a relation between the multiplicity m of the second
eigenvalue {\lambda}2 of a Laplacian on a graph G, tight mappings of G and a
discrete analogue of Courant's nodal line theorem. For a certain class of
graphs, we show that the m-dimensional eigenspace of {\lambda}2 is tight and
thus defines a tight mapping of G into an m-dimensional Euclidean space. The
tightness of the mapping is shown to set Colin de Verdi\`ere's upper bound on
the maximal {\lambda}2-multiplicity, where chr({\gamma}(G)) is the chromatic
number and {\gamma}(G) is the genus of G.
