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Luchando para dibujar un gráfico de ruta en TikZ

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Luchando para dibujar un gráfico de ruta en TikZ

Como principiante aprendiendo TikZ, probé lo siguiente:

\documentclass[border=0.2cm]{standalone}
\usepackage{tikz}
\usetikzlibrary{automata, positioning}

\begin{document}
\begin{tikzpicture} [draw=black,
node distance = 3cm, 
on grid, 
auto,
every loop/.style={stealth-}]

\node (e1) [state] {$E$};
\node (c1) [state, right = of e1] {$C$};
\node (a1) [state, right = of c1] {$A$};
\node (t1) [state, below = of c1] {$T1$};
\node (a2) [state, right = of a1] {$A$};
\node (c2) [state, right = of a2] {$C$};
\node (e2) [state, right = of c2] {$E$};    
\node (t2) [state, below = of c2] {$T2$};

% Arrows
\path [-stealth, thick]
(e1) edge node {$e^2$}   (t1)
(c1) edge node {$c^2$}   (t1)
(a1) edge node {$h^2$}   (t1)
(e1) edge [loop above]  node {1}()
(c1) edge [loop above]  node {1}()
(a1) edge [loop above]  node {1}()
(e2) edge node {$e^2$}   (t2)
(c2) edge node {$c^2$}   (t2)
(a2) edge node {$h^2$}   (t2)
(e2) edge [loop above]  node {1}()
(c2) edge [loop above]  node {1}()
(a2) edge [loop above]  node {1}()
(a1) edge [bend left]  node {1}(a2)
(c1) edge [bend left]  node {1}(c2);
\end{tikzpicture}
\end{document}

Y este es el resultado actual:

ingrese la descripción de la imagen aquí

Mejoras necesarias:

  1. Cambie los dos caminos de flexión por unos con flechas bidireccionales;
  2. Eleve un poco más el camino de curvatura más largo para evitar que se superponga;
  3. Cambie los dos nodos T1 y T2 en la parte inferior de círculo a rectángulo;
  4. Alinee horizontalmente esas seis etiquetas (e^2, c^2, h^2, ...).

¡Gracias!

Respuesta1

¡Aquí tienes!

autómatas con mejoras

\documentclass[border=0.2cm]{standalone}
% https://tex.stackexchange.com/questions/678743/struggling-in-drawing-a-path-graph-in-tikz

\usepackage{tikz}
\usetikzlibrary{automata, positioning}

\begin{document}
\begin{tikzpicture} [draw=black,
node distance = 3cm, 
on grid, 
auto,
every loop/.style={stealth-},
myrect/.style={rectangle,draw,inner sep=8pt}]

\node (e1) [state] {$E$};
\node (c1) [state, right = of e1] {$C$};
\node (a1) [state, right = of c1] {$A$};
\node (t1) [myrect, below = of c1] {$T1$};
\node (a2) [state, right = of a1] {$A$};
\node (c2) [state, right = of a2] {$C$};
\node (e2) [state, right = of c2] {$E$};    
\node (t2) [myrect, below = of c2] {$T2$};

% Arrows
\path [-stealth, thick]
(e1) edge node[midway,right=3pt] {$e^2$}   (t1)
(c1) edge node[midway,right] {$c^2$}   (t1)
(a1) edge node[midway,right] {$h^2$}   (t1)
(e1) edge [loop above]  node {1}()
(c1) edge [loop above]  node {1}()
(a1) edge [loop above]  node {1}()
(e2) edge node[midway,right] {$e^2$}   (t2)
(c2) edge node[midway,right] {$c^2$}   (t2)
(a2) edge node[midway,right=2pt] {$h^2$}   (t2)
(e2) edge [loop above]  node {1}()
(c2) edge [loop above]  node {1}()
(a2) edge [loop above]  node {1}()
(a1) edge [<->,bend left]  node {1}(a2)
(c1) edge [<->,bend left=50]  node {1}(c2);
\end{tikzpicture}
\end{document}

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