[Tex/LaTex] Strike-through Tilde Accent

Question

I am working with graphs (V, E) which have a fixed number of common neighbours and common non-neighbours for each pair of adjacent vertices, and non-adjacent vertices as well. To denote these four invariants, I'm using the following symbols:

I'm not too keen on it though (I don't like how _\sim and _\nsim look). I'm considering using the \tilde accent, but I would like an analogous \nottilde accent, that is, a stricken-through \tilde accent:

I'd imagine creating such a command would involve quite a bit of hassle, especially to be compatible with \widetilde. I have no idea how to go about creating it (I used paint for the picture above).

I'm also open to other suggestions for this notation! Thanks.

Answer 1

What about this?

\documentclass{article}
\usepackage{amsmath,amssymb}
\def\nottilde#1{\overset{\ifx#1f\hspace{.5ex}\fi\lower0.8ex\hbox{\tiny$\nsim$}}{#1}}
\def\xtilde#1{\overset{\ifx#1f\hspace{.5ex}\fi\lower0.8ex\hbox{\tiny$\sim$}}{#1}}
\begin{document}
$\tilde{e}\xtilde{e}\nottilde{e}\xtilde{f}\nottilde{f}$
\end{document}