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 talk, we will show an exact relation between the maximum dimension that a multigraph can be realized as a super stable tensegrity and Colin de Verdière 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. Our approach can also be used to show that for any fixed \d, there is an infinite family of \3-regular graphs that can be realized as \d-dimensional super stable injective tensegrities. This is a joint work with Shin-ichi Tanigawa.