The real equiangular tight frames obtained from rank $3$ graphs

Abstract: We present all nontrivial real equiangular tight frames ${\varphi_m}_{m=1}^M$ in $\mathbb{R}^N$ obtained as spherical embeddings of primitive rank $3$ graphs on $M$ vertices, and those such that one of their associated $M$ strongly regular graphs on $M-1$ vertices is a primitive rank $3$ graph.