Drawing a circle graph with TIKZ with foreach placement and paths, yet the inbound for edges is off

Question

I want to draw a circle using TIKZ and instead of manually placing the nodes and connecting the nodes I wanted to use loops as any sane person would. Now when I wrote these, the incoming edge seems to be going to some point slightly of the node instead of to its core.

In the example, I included a version with the path manually written out. I am losing my sanity here :D Anyone got any idea as to what is happening here? Any style critique is also very welcome!

\documentclass[margin=10pt]{standalone}
\usepackage{tikz}
    \usetikzlibrary{automata}
                
\begin{document}
\begin{tikzpicture}[nodes=state]
\def \number {8}
\def \radius {2cm}
\def \degree {360/\number}

\foreach \s in {1,...,\number}
{
    \node at ({\degree * (\s -1)}:\radius) (\s) {$u_\s$};
}

\foreach \s in {1,...,\number}
{
    \pgfmathsetmacro\result{Mod( (\s), \number)+1}
    \path (\s) edge[bend right = 15] (\result);
}
\end{tikzpicture}

\begin{tikzpicture}[nodes=state]
\def \number {8}
\def \radius {2cm}
\def \degree {360/\number}

\foreach \s in {1,...,\number}
{
    \node at ({\degree * (\s -1)}:\radius) (\s) {$u_\s$};
}

          \path (1) edge[bend right = 15] (2)
%                   edge (5)
                (2) edge[bend right = 15] (3)
%                   edge (6)
                (3) edge[bend right = 15] (4)
%                   edge (7)
                (4) edge[bend right = 15] (5)
%                   edge (8)
                (5) edge[bend right = 15] (6)
                (6) edge[bend right = 15] (7)
                (7) edge[bend right = 15] (8)
                (8) edge[bend right = 15] (1)
                    ;
\end{tikzpicture}
\end{document}

Answer 1

You need

\pgfmathtruncatemacro\result{Mod( (\s), \number)+1} 

to drop .0, which gets interpreted as a node anchor (the east anchor). Or use evaluate with int.

\documentclass[margin=10pt]{standalone}
\usepackage{tikz}
\usetikzlibrary{automata}
                
\begin{document}
\begin{tikzpicture}[nodes=state]
\def \number {8}
\def \radius {2cm}
\def \degree {360/\number}

\foreach \s in {1,...,\number}
{
    \node at ({\degree * (\s -1)}:\radius) (\s) {$u_\s$};
}

\foreach \s [evaluate=\s as \result using {int(Mod( (\s), \number)+1)}]in {1,...,\number}
{
    \path (\s) edge[bend right = 15] (\result);
}
\end{tikzpicture}
\end{document}

Answer 2

If if the problem is just to arrange the circles on the circle, this can be done relative simple:

\documentclass[tikz, margin=10pt]{standalone}

\begin{document}
    \begin{tikzpicture}[
C/.style = {circle, draw, fill=white, minimum size=7mm, 
            inner sep=0pt, outer sep=0pt}
                        ]
\def \number {8}
\def \radius {2cm}
\def \degree {360/\number}
% circle
\draw   (0,0)   circle[radius=\radius];
% nodes on circle
    \foreach \i [count=\j from 0] in {1,...,\number}
\node (n\i) [C] at (\j*\degree:\radius) {$u_\i$};
    \end{tikzpicture}
\end{document}

Or do I miss/misunderstood something?