  A super stable tensegrity introduced by Connelly in 1982 is a globally rigid
discrete structure made from stiff bars or struts connected by cables with
tension. In this paper we show an exact relation between the maximum dimension
that a multigraph can be realized as a super stable tensegrity and Colin de
Verdi\`{e}re number~$\nu$ from spectral graph theory. As a corollary we obtain
a combinatorial characterization of multigraphs that can be realized as
3-dimensional super stable tensegrities.
