Two versions with help of library automata:
\documentclass{beamer}
\usepackage{tikz}
\usetikzlibrary{arrows.meta, automata, positioning, quotes}
\begin{document}
\centering
\begin{tikzpicture}[
shorten < = 1mm, shorten > = 1mm,
node distance = 33mm, on grid, auto,
every path/.style = {bend left, -Latex}
]
\node[state] (A) {A};
\node[state] (B) [right=of A] {B};
\node[state] (C) [below=of A] {C};
\node[state] (D) [right=of C] {D};
%
\path[->] (A) edge ["e"] (B)
(B) edge (D)
(D) edge (C)
(C) edge ["h"] (A)
%
(A) edge (C)
(C) edge (D)
(D) edge ["g"] (B)
(B) edge ["f"] (A);
\end{tikzpicture}
\begin{tikzpicture}[
shorten < = 1mm, shorten > = 1mm,
node distance = 33mm, on grid, auto,
every path/.style = {-Latex},
sx+/.style = {xshift=1 mm},
sy+/.style = {yshift=1 mm},
sx-/.style = {xshift=-1 mm},
sy-/.style = {yshift=-1 mm},
]
\node[state] (A) {A};
\node[state] (B) [right=of A] {B};
\node[state] (C) [below=of A] {C};
\node[state] (D) [right=of C] {D};
%
\path[->] ([sy+] A.east) edge ["e"] ([sy+] B.west)
([sx+] B.south) edge ([sx+] D.north)
([sy-] D.west) edge ([sy-] C.east)
([sx-] C.north) edge ["h"] ([sx-] A.south)
%
([sx+] A.south) edge ([sx+] C.north)
([sy+] C.east) edge ([sy+] D.west)
([sx-] D.north) edge ["g"] ([sx-] B.south)
([sy-] B.west) edge ["f"] ([sy-] A.east);
\end{tikzpicture}
\end{document}

Edit:
Added nicer arrows positions in second image
Addendum:
Version which doesn't follow to image shown in question but to code:
\documentclass{beamer}
\usepackage{tikz}
\usetikzlibrary{arrows.meta, automata, calc, positioning, quotes}
\begin{document}
\centering
\begin{tikzpicture}[
shorten < = 1mm, shorten > = 1mm,
node distance = 22mm, on grid, auto,
every path/.style = {-Latex},
state/.append style = {draw=pink!30!black, fill=pink!30, minimum size=8mm},
sx+/.style = {xshift=1 mm},
sy+/.style = {yshift=1 mm},
sx-/.style = {xshift=-1 mm},
sy-/.style = {yshift=-1 mm},
]
\node[state] (A) {A};
\node[state] (B) [right=of A] {B};
\node[state] (C) [below right=of A] {C};
\node[state] (D) [right=of C] {D};
%
\path[->] ([sy+] A.east) edge ["e"] ([sy+] B.west)
([sx+] B.south east) edge ([sx+] D.north west)
([sy-] D.west) edge ([sy-] C.east)
([sx-] C.north west) edge ["h"] ([sx-] A.south east)
%
([sx+] A.south east) edge ([sx+] C.north west)
([sy+] C.east) edge ([sy+] D.west)
([sx-] D.north west) edge ["g"] ([sx-] B.south east)
([sy-] B.west) edge ["f"] ([sy-] A.east);
\end{tikzpicture}
\end{document}
