Q:

problem with creating a graph using tikz

I have a little problem. I have create with latex a graph. Here is my code
\[
\begin{tikzpicture}[->,>=stealth,shorten >=1pt,auto,node distance=2.5cm,
                    semithick]
  \tikzset{every state/.append style={fill=red,draw=none,text=white}}

  \node[state]         (A)              {$\{\omega\}$};
  \node[state]         (B) [below=of A] {$A_{2}(1)$};
  \node[state]         (C) [below=of B] {$A_{1}(1)$};
  \node[state]         (D) [below=of C] {$\{\omega\}$};
  \node[state]         (F) [right=of B] {$A_{2}(2)$};
  \node[state]         (E) [above=of F] {$\{\omega\}$};
  \node[state]         (G) [below=of F] {$A_{1}(2)$};
  \node[state]         (H) [below=of G] {$\{\omega\}$};
  \node[state]         (J) [right=of F] {$A_{2}(m-1)$};
  \node[state]         (I) [above=of J] {$\{\omega\}$};
  \node[state]         (K) [below=of J] {$A_{1}(m-1)$};
  \node[state]         (L) [below=of K] {$\{\omega\}$};
  \node[state]         (M) [right=of J] {$A_{2}(m)$};
  \node[state]         (N) [right=of K] {$A_{1}(m)$};
  \node[state]         (O) [above=of M] {$\{\omega\}$};
  \node[state]         (P) [below=of N] {$\{\omega\}$};

  \path (B) edge              node {$\mathbf{Q}_{A_{2}\{\omega\}}$} (A)
            edge [loop left]  node {$\QAt$}                         (B)
            edge              node {$\QAto$}                        (C)
        (C) edge [loop left]  node {$\QAo$}                         (C)
            edge              node {$\mathbf{Q}_{A_{1}\{\omega\}}$} (D)
            edge [right]      node {$\QAot$}                        (F)
        (F) edge              node {$\mathbf{Q}_{A_{2}\{\omega\}}$} (E)
            edge [loop left]  node {$\QAt$}                         (F)
            edge              node(aux) {$\QAto$}                        (G)
        (G) edge [loop left]  node {$\QAo$}                         (G)
            edge              node {$\mathbf{Q}_{A_{1}\{\omega\}}$} (H)
        (J) edge              node {$\mathbf{Q}_{A_{2}\{\omega\}}$} (I)
            edge [loop left]  node {$\QAt$}                         (J)
            edge              node {$\QAto$}                        (K)
        (K) edge [loop left]  node {$\QAo$}                         (K)
            edge              node {$\mathbf{Q}_{A_{1}\{\omega\}}$} (L)
            edge [right]      node {$\QAot$}                        (M)
        (M) edge [loop left]  node {$\QAt$}                         (M)
            edge              node {$\QAtw$}                        (O)
            edge              node {$\QAto$}                        (N)
        (N) edge [loop left]  node {$\QAo$}                         (N)
            edge              node {$\QAow + \QAot\mathbf{1}$}      (P);
 \node[right=2mm of aux,font=\bfseries\Huge]{\dots};
\end{tikzpicture}
\]
\caption{\"Ubergangsgraph von $X$}\label{Abbildung3}
\end{figure}

where
\newcommand{\QAt}{\mathbf{Q}_{A_{2}A_{2}}}
\newcommand{\QAo}{\mathbf{Q}_{A_{1}A_{1}}}
\newcommand{\QAot}{\mathbf{Q}_{A_{1}A_{2}}}
\newcommand{\QAto}{\mathbf{Q}_{A_{2}A_{1}}}
\newcommand{\QAtC}{\mathbf{Q}_{A_{2}C}}
\newcommand{\QAtw}{\mathbf{Q}_{A_{2}\{\omega\}}}
\newcommand{\QAow}{\mathbf{Q}_{A_{1}\{\omega\}}}

The graph looks as follows

My question is how I can use ovals instead of cirlces, such that the nodes all have the same size. It should look like as follows

A:

Too long for a comment. ellipse does work. To decrease the horizontal space, I changed the looseness of the loops, decreased the node distance and stacked the lower right edge label. Note also that the loops increase the bounding box unnecessarily such that I add a bounding box by hand. (With the lower looseness of the loops the problem is less severe.) To make the wider ellipses approximately equal, you could play with inner xsep. Alternatively, you could use \makeboxes.
\documentclass{article}
\usepackage[margin=1in]{geometry}
\usepackage{amsmath,amssymb}
\usepackage{tikz}
\usetikzlibrary{shapes.geometric,automata,positioning} 
\newcommand{\QAt}{\mathbf{Q}_{A_{2}A_{2}}}
\newcommand{\QAo}{\mathbf{Q}_{A_{1}A_{1}}}
\newcommand{\QAot}{\mathbf{Q}_{A_{1}A_{2}}}
\newcommand{\QAto}{\mathbf{Q}_{A_{2}A_{1}}}
\newcommand{\QAtC}{\mathbf{Q}_{A_{2}C}}
\newcommand{\QAtw}{\mathbf{Q}_{A_{2}\{\omega\}}}
\newcommand{\QAow}{\mathbf{Q}_{A_{1}\{\omega\}}}
\begin{document}
\begin{figure}[htb]
\centering
\begin{tikzpicture}[->,>=stealth,shorten >=1pt,auto,node distance=2cm,
                    semithick,
 every state/.append style={fill=red,draw=none,text=white,ellipse},
 every loop/.append style={looseness=5}]
  \path[use as bounding box] (-2.7,0.45) rectangle (15,-10.65); 
  \pgfmathsetmacro{\mywidth}{(width("$A_{2}(m-1)$")-width("$A_{2}(1)$"))/4}
  \node[state]         (A)              {$\{\omega\}$};
  \node[state,inner xsep=\mywidth]         (B) [below=of A] {$A_{2}(1)$};
  \node[state,inner xsep=\mywidth]         (C) [below=of B] {$A_{1}(1)$};
  \node[state]         (D) [below=of C] {$\{\omega\}$};
  \node[state,inner xsep=\mywidth]         (F) [right=of B] {$A_{2}(2)$};
  \node[state]         (E) [above=of F] {$\{\omega\}$};
  \node[state,inner xsep=\mywidth]         (G) [below=of F] {$A_{1}(2)$};
  \node[state]         (H) [below=of G] {$\{\omega\}$};
  \node[state,inner xsep=-\mywidth]         (J) [right=of F] {$A_{2}(m-1)$};
  \node[state]         (I) [above=of J] {$\{\omega\}$};
  \node[state,inner xsep=-\mywidth]         (K) [below=of J] {$A_{1}(m-1)$};
  \node[state]         (L) [below=of K] {$\{\omega\}$};
  \node[state,inner xsep=\mywidth]         (M) [right=of J] {$A_{2}(m)$};
  \node[state,inner xsep=\mywidth]         (N) [right=of K] {$A_{1}(m)$};
  \node[state]         (O) [above=of M] {$\{\omega\}$};
  \node[state]         (P) [below=of N] {$\{\omega\}$};

  \path (B) edge              node {$\mathbf{Q}_{A_{2}\{\omega\}}$} (A)
            edge [loop left]  node {$\QAt$}                         (B)
            edge              node {$\QAto$}                        (C)
        (C) edge [loop left]  node {$\QAo$}                         (C)
            edge              node {$\mathbf{Q}_{A_{1}\{\omega\}}$} (D)
            edge [right]      node {$\QAot$}                        (F)
        (F) edge              node {$\mathbf{Q}_{A_{2}\{\omega\}}$} (E)
            edge [loop left]  node {$\QAt$}                         (F)
            edge              node(aux) {$\QAto$}                        (G)
        (G) edge [loop left]  node {$\QAo$}                         (G)
            edge              node {$\mathbf{Q}_{A_{1}\{\omega\}}$} (H)
        (J) edge              node {$\mathbf{Q}_{A_{2}\{\omega\}}$} (I)
            edge [loop left]  node {$\QAt$}                         (J)
            edge              node {$\QAto$}                        (K)
        (K) edge [loop left]  node {$\QAo$}                         (K)
            edge              node {$\mathbf{Q}_{A_{1}\{\omega\}}$} (L)
            edge [right]      node {$\QAot$}                        (M)
        (M) edge [loop left]  node {$\QAt$}                         (M)
            edge              node {$\QAtw$}                        (O)
            edge              node {$\QAto$}                        (N)
        (N) edge [loop left]  node {$\QAo$}                         (N)
            edge              node[align=left] {$\hphantom{+}\QAow$\\
            $+ \QAot\mathbf{1}$}      (P);
 \node[right=2mm of aux,font=\bfseries\Huge]{\dots};
\end{tikzpicture}
\caption{\"Ubergangsgraph von $X$.}\label{Abbildung3}
\end{figure}
\end{document}

A:

mostly off-topic, but it can be helpful:
\documentclass[tikz,margin=3.141592]{standalone}
\usetikzlibrary{arrows.meta,
                chains,
                positioning,
                quotes,
                shapes.geometric}

\newcommand{\QAt}{\mathbf{Q}_{A_{2}A_{2}}}
\newcommand{\QAo}{\mathbf{Q}_{A_{1}A_{1}}}
\newcommand{\QAot}{\mathbf{Q}_{A_{1}A_{2}}}
\newcommand{\QAto}{\mathbf{Q}_{A_{2}A_{1}}}
\newcommand{\QAtC}{\mathbf{Q}_{A_{2}C}}
\newcommand{\QAtw}{\mathbf{Q}_{A_{2}\{\omega\}}}
\newcommand{\QAow}{\mathbf{Q}_{A_{1}\{\omega\}}}

\begin{document}
    \begin{tikzpicture}[auto,
%   scale=0.8,
%   transform shape,
node distance = 15mm and 35mm, on grid,
  start chain = going below,
 state/.style = {ellipse, minimum height=7mm, inner xsep=0pt,
                 fill=red, text=white,
                 on chain},
every edge/.append style = {draw,-Stealth},
every loop/.append style = {looseness=4}
                        ]
\begin{scope}[every node/.style = {state}]
  \node (A) {$\{\omega\}$};
  \node (B) {$A_{2}(1)$};
  \node (C) {$A_{1}(1)$};
  \node (D) {$\{\omega\}$};
%
  \node (E) [right=of A]    {$\{\omega\}$};
  \node (F) {$A_{2}(2)$};
  \node (G) {$A_{1}(2)$};
  \node (H) {$\{\omega\}$};
%
  \node (I) [right=of E]    {$\{\omega\}$};
  \node (J) {$A_{2}(m{-}1)$};
  \node (K) {$A_{1}(m{-}1)$};
  \node (L) {$\{\omega\}$};
%
  \node (M) [right=of I]    {$\{\omega\}$};
  \node (N) {$A_{2}(m)$};
  \node (O) {$A_{1}(m)$};
  \node (P) {$\{\omega\}$};
\end{scope}
%
\path   (B) edge ["$\mathbf{Q}_{A_{2}\{\omega\}}$"] (A)
            edge [loop left,"$\QAt$"]               (B)
            edge ["$\QAto$"]                        (C)
        (C) edge [loop left,"$\QAo$"]               (C)
            edge ["$\mathbf{Q}_{A_{1}\{\omega\}}$"] (D)
            edge ["$\QAot$" ']                      (F)
        (F) edge ["$\mathbf{Q}_{A_{2}\{\omega\}}$"] (E)
            edge [loop left,"$\QAt$"]               (F)
            edge    node (aux) {$\QAto$}            (G)
        (G) edge [loop left,"$\QAo$"]               (G)
            edge ["$\mathbf{Q}_{A_{1}\{\omega\}}$"] (H)
        (J) edge ["$\mathbf{Q}_{A_{2}\{\omega\}}$"] (I)
            edge [loop left,,"$\QAt$"]              (J)
            edge ["$\QAto$"]                        (K)
        (K) edge [loop left,"$\QAo$"]               (K)
            edge ["$\mathbf{Q}_{A_{1}\{\omega\}}$"] (L)
            edge ["$\QAot$" ']                      (N)
        (M) edge [loop left,"$\QAt$"]               (M)
            edge ["$\QAtw$"]                        (N)
        (N) edge ["$\QAto$"]                        (O)
        (O) edge [loop left,"$\QAo$"]               (O)
            edge ["$\QAow + \QAot\mathbf{1}$"]      (P);
\draw[ultra thick,loosely dotted,shorten <=2mm] (aux) -- + (1.5,0);
\end{tikzpicture}
\end{document}

i don't know, if this image isn't wide than \textwidth since the page layout of your document is unknown. however, you can adjust image width with uncomment lines with scale=... and transform shape and adjust image size accordingly :-)

