Consider this document:
```
\documentclass{beamer}
\usepackage{tikz}
\usetikzlibrary{arrows.meta}
\makeatletter
\newcommand*{\slideinframe}{\number\beamer@slideinframe}
\makeatother
\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", "6/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", "4/E", "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]  \pgfmathparse{\mylistA[\slideinframe-1]}\pgfmathresult}]  (A) at (0,5) {A};
    \node[label={[xshift=0em, yshift=-1em, text=black] \pgfmathparse{\mylistB[\slideinframe-1]}\pgfmathresult}]  (B) at (5,5) {B};
    \node[label={[xshift=0em, yshift=-1em, text=black] \pgfmathparse{\mylistC[\slideinframe-1]}\pgfmathresult}]  (C) at (10,5) {C};
    \node[label={[xshift=0em, yshift=-6em, text=black] \pgfmathparse{\mylistD[\slideinframe-1]}\pgfmathresult}]  (D) at (0,0) {D};
    \node[label={[xshift=0em, yshift=-6em, text=black] \pgfmathparse{\mylistE[\slideinframe-1]}\pgfmathresult}]  (E) at (5,0) {E};
    \node[label={[xshift=0em, yshift=-6em, text=black]  \pgfmathparse{\mylistF[\slideinframe-1]}\pgfmathresult}]  (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}
```
I would like to highlight an edge on some of the transitions and also change the thickness of an edge permanently on others. For example,
Make E->D edge red on transition 3 only. Make E->B red on transition 4 only. Make E->F red on transition 5 only. Make E->C red on transition 6 only.  Make E->F thick and black on transitions 7 onwards and make F->B red on transition 7 only.
Here an example on how to change the line colour and thickness for one edge. I'll leave the others as exercise for you :)
Please note that you can only have as many overlays as there are items in your list. You have six items, if you want to have seven overlays, you need to add a 7th item.
```
\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,text=black},
              ]
    \path [-] (A) edge node {$1$} (B);
    \path [-] (D) edge node {$2$} (B);
    \path [-] (A) edge node {$3$} (D);
    \draw [-,alt=<5>{red}{black},alt=<6->{ultra thick}{}] (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}
```
