\begin{equation}
    {\tilde{\mathcal{A}}_{i_{1} \ldots i_{k}}}= \begin{cases}\frac{1}{(k-1) !} \prod_{1 \leqslant j \leqslant k} \frac{1}{\sqrt[k]{d_{i_{j}}}} & \text { if }\left\{v_{i_{1}}, \ldots, v_{i_{k}}\right\} \in E \\ 0 & \text { otherwise }\end{cases}.
\label{Eq:THNN2}
\notag
\end{equation}
