You can reuse Schrödinger's cat's style for bent arrows. This style gives good results even on curved paths and accepts an optional argument, defaulting to 0.5 (= middle), to indicate where the arrow should lie on the path on which it is placed. With this style, the arrow can be drawn with simply:
\draw[attach arrow] (a2) -- (a5);
You may specify attach arrow=0.5 if you want to be explicit about the position of the arrow on the edge from a2 to a5.
I also used the scope environment to reduce redundancy in your example and
\draw[green!80!black, attach arrow] (a2) -- (a5)
node[pos=0.5, below, black] {$U$};
to automatically place the U below the middle of the edge from a2 to a5 (no hardcoding of coordinates here). If you want to place it a little lower, you can add \usetikzlibrary{positioning} to the preamble and replace the above two lines with, for instance:
\draw[green!80!black, attach arrow] (a2) -- (a5) coordinate[pos=0.5] (mid);
\node[below=0.3cm of mid] {$U$};
Also, pos=0.5 may be replaced with midway, but this is not tremendously useful. Full code:
\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{arrows.meta, bending, decorations.markings}
% https://tex.stackexchange.com/a/524935/73317 (Schrödinger's cat)
\tikzset{
attach arrow/.style={
decoration={
markings,
mark=at position 0 with {\pgfextra{%
\pgfmathsetmacro{\tmpArrowTime}{\pgfkeysvalueof{/tikz/arc arrow/length}/(\pgfdecoratedpathlength)}%
\xdef\tmpArrowTime{\tmpArrowTime}}},
mark=at position {#1-3*\tmpArrowTime} with {\coordinate(@1);},
mark=at position {#1-2*\tmpArrowTime} with {\coordinate(@2);},
mark=at position {#1-1*\tmpArrowTime} with {\coordinate(@3);},
mark=at position {#1+\tmpArrowTime/2} with {\coordinate(@4);
\draw[-{Stealth[length=\pgfkeysvalueof{/tikz/arc arrow/length},bend]}]
plot[smooth] coordinates {(@1) (@2) (@3) (@4)};},
},
postaction=decorate,
},
% Default arrow location: in the middle of the path
attach arrow/.default=0.5,
arc arrow/length/.initial=2mm,
}
\begin{document}
\begin{tikzpicture}[
thick,
acteur/.style={
circle,
thick,
fill=black,
inner sep=2pt,
minimum size=0.2cm
}]
\begin{scope}[nodes={acteur}]
\node (a1) at (0,0) [label=below:6] {};
\node (a2) at (1.5,0) [label=below:1] {};
\node (a3) at (1.5,1.5) [label=above:4] {};
\node (a4) at (0,1.5) [label=above:5] {};
\node (a5) at (3,0) [label=below:2] {};
\node (a6) at (4.5,0) [label=below:7] {};
\node (a7) at (3,1.5) [label=above:3] {};
\node (a8) at (4.5,1.5) [label=above:8] {};
\end{scope}
\begin{scope}[color=red]
\draw (a1) -- (a2);
\draw (a2) -- (a3);
\draw (a3) -- (a4);
\draw (a6) -- (a5);
\draw (a5) -- (a7);
\draw (a8) -- (a7);
\draw (a3) -- (a7);
\end{scope}
\draw[green!80!black, attach arrow] (a2) -- (a5)
node[pos=0.5, below, black] {$U$};
\end{tikzpicture}
\end{document}
With the alternative based on \usetikzlibrary{positioning} and:
\draw[green!80!black, attach arrow] (a2) -- (a5) coordinate[pos=0.5] (mid);
\node[below=0.3cm of mid] {$U$};
you would get:
Note: there are other ways to draw the graph (e.g., TikZ matrices and \usetikzlibrary{graphs}), but the present question is about the arrow, and better tackle one problem at a time, especially when beginning. :-)
