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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 $i\neqj$ is $-1$ if $v_i\sim v_j$ and $1$ otherwise, and whose diagonal entries are$0$. We show that the proportion of simple graphs $G_n$ such that$\det(S(G_n))\geq n-1$ tends to one as $n$ tends to infinity.

Determinants of Seidel matrices and a conjecture of Ghorbani