I am trying to draw two forest and I've been able to. What I'd like to add now is a Equivalence arrow (\Leftrightarrow) in the middle of those, but well aligned.
Currently I have the following code:
\documentclass[a4paper,12pt]{article}
\usepackage{color,forest,tikz,amsmath,amsbsy,amsfonts,mathtools,amssymb,amsthm}
\begin{document}
\begin{center}
\begin{forest}
for tree = {draw,circle,edge={black,thick},inner sep=2pt, minimum width= .25cm,
font = \small, s sep = 1cm}
[,fill=black, label = {u}
[,fill=red]
[,fill=red]
]
\end{forest}
$\qquad \Rightarrow \qquad$
\begin{forest}
for tree = {draw,circle,edge={black,thick},inner sep=2pt, minimum width= .25cm,
font = \small, s sep = 1cm}
[,fill=red, label = {u}
[,fill=black]
[,fill=black]
]
\end{forest}
\end{center}
\end{document}
And this gives me the following Output:
I would like to replace the Rightarrow with Leftrightarrow (I can do that by myself) well aligned with both the trees. Besides from this, is it also possible to paint half the Leftrightarrow as red and other half as black? If so, my desired output would be something like this:

If it's not possible to draw a Leftrightarrow with two colors I would also accept a normal leftrightarrow!
Thanks for any help in advance!





\begin{adjustbox}{valign=m}see e.g. https://tex.stackexchange.com/a/320316/250119 – user202729 Jun 05 '22 at 15:37