Using the `overlay-beamer-styles` library, you can add things like `alt=<2->{red}{black},text=white` to your node to change the colour on certain overlays
You might also want to ensure that your labels above and blow the nodes all have the same height with something like `minimum height=1.7cm` to avoid the image jumping around.
```
\documentclass{beamer}
\usepackage{tikz}
\usetikzlibrary{arrows.meta}
\usetikzlibrary{overlay-beamer-styles}
\def\mylistE{{"$\infty/$null", 0, 0, 0, 0, 0, 0}}
\def\mylistD{{"$\infty/$null", "$\infty/$null", "3/E", "3/E", "3/E", "3/E", "3/E"}}
\def\mylistB{{"$\infty/$null", "$\infty/$null", "$\infty/$null", "6/E", "5/F", "5/F", "5/F"}}
\def\mylistF{{"$\infty/$null", "$\infty/$null", "$\infty/$null", "$\infty/$null", "2/E", "2/E", "2/E"}}
\def\mylistC{{"$\infty/$null", "$\infty/$null", "$\infty/$null", "$\infty/$null", "$\infty/$null", "4/E", "4/E"}}
\def\mylistA{{"$\infty/$null", "$\infty/$null", "$\infty/$null", "$\infty/$null", "$\infty/$null", "3/D"}}
\begin{document}
\begin{frame}
\frametitle{Demonstration}
\begin{tikzpicture}
\begin{scope}[every node/.style={fill=black, text=white, circle,thick,draw, minimum size=1.2cm}]
\node[label={[xshift=0em, yshift=-1em, text=black,minimum height=1.7cm] \pgfmathparse{\mylistA[ \insertslidenumber-1]}\pgfmathresult}] (A) at (0,5) {A};
\node[label={[xshift=0em, yshift=-1em, text=black,minimum height=1.7cm] \pgfmathparse{\mylistB[ \insertslidenumber-1]}\pgfmathresult}] (B) at (5,5) {B};
\node[label={[xshift=0em, yshift=-1em, text=black,minimum height=1.7cm] \pgfmathparse{\mylistC[ \insertslidenumber-1]}\pgfmathresult}] (C) at (10,5) {C};
\node[label={[xshift=0em, yshift=-6em, text=black,minimum height=1.7cm] \pgfmathparse{\mylistD[ \insertslidenumber-1]}\pgfmathresult},alt=<6->{red}{black},text=white] (D) at (0,0) {D};
\node[label={[xshift=0em, yshift=-6em, text=black,minimum height=1.7cm] \pgfmathparse{\mylistE[ \insertslidenumber-1]}\pgfmathresult},alt=<2->{red}{black},text=white] (E) at (5,0) {E};
\node[label={[xshift=0em, yshift=-6em, text=black,minimum height=1.7cm] \pgfmathparse{\mylistF[ \insertslidenumber-1]}\pgfmathresult},alt=<5->{red}{black},text=white] (F) at (10,0) {F} ;
\end{scope}
\begin{scope}[>={Stealth[black]},
every node/.style={fill=white,circle},
every edge/.style={draw=red,very thick}]
\path [-] (A) edge node {$1$} (B);
\path [-] (D) edge node {$2$} (B);
\path [-] (A) edge node {$3$} (D);
\path [-] (D) edge node {$3$} (E);
\path [-] (E) edge node {$2$} (F);
\path [-] (E) edge node {$6$} (B);
\path [-, pos=0.25] (E) edge node {$4$} (C);
\path [-] (B) edge node {$3$} (C);
\path [-, pos=0.25] (B) edge node {$5$} (F);
\path [-] (F) edge node {$4$} (C);
\end{scope}
\end{tikzpicture}
\pause[6]
\end{frame}
\end{document}
```
