Determinants of Seidel matrices and a conjecture of Ghorbani

Let $G_n$ be a simple graph on $V_n=\{v_1,\dots ,v_n\}$. The Seidel matrix $S(G_n)$ of $G_n$ is the $n\times n$ matrix whose $(ij)$'th entry, for $i\neq j$is$-1$if$v_i\sim v_j$and$1$otherwise,andwhosediagonalentriesare$0$\mathrm{.}Weshowthattheproportionofsimplegraphs$G_n$suchthat$\det(S(G_n))\geq n-1$tendstooneas$n$ tends to infinity.