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 Verdière number~$ν$ from spectral graph theory. As a corollary we obtain a combinatorial characterization of multigraphs that can be realized as 3-dimensional super stable tensegrities.