[Tex/LaTex] Creating large star graph

graphicstikz-graphdrawingtikz-pgf

I'm trying to create a star graph in Latex. My graph may have an arbitrary large number of vertices, so I'm trying to incorporate this fact in the drawing.
This is what I have done so far:

%My Macros:
\usepackage{amsmath,amsthm,amssymb,bbm,mathtools}
\usepackage{xcolor}
\usepackage{algorithm}
\usepackage[noend]{algpseudocode}
\usepackage{blkarray} %for stating column index
\usepackage{tikz}

\begin{document}
\begin{figure}
\centering
\caption{Star Graph}
\begin{tikzpicture}
\label{star_poa}
\def \n {20}
\def \N {8}
\def \radius {3cm}
\def \rd {1mm}
\def \rer {4mm}

\def \margin {8} % margin in angles, depends on the radius

\node[draw, circle] at (360:0mm) {$u_*$};
  \node[draw, circle] at ({360/\n *\n / 4}:\radius) {$u_{1}$};
    \node[draw, circle] at ({360/4 - 360/\n * (2 - 1)}:\radius) {$u_2$};
        \node[draw, circle] at ({360/4 - 360/\n * (3 - 1)}:\radius) {$u_3$};
        \node[draw, circle] at ({360/4 - 360/\n * (4 - 1)}:\radius) {$u_4$};

    \node[draw, circle] at ({360/4 + 360/\n * (2 - 1)}:\radius) {$u_t$};        

\path
({360/4 - 360/\n * (1 - 1)}:{\rer}) edge node [left] {a} ({360/4 - 360/\n * (1 - 1)}:\radius-\margin-\rd);

\path
({360/4 - 360/\n * (2 - 1)}:{\rer}) edge node [left] {a} ({360/4 - 360/\n * (2 - 1)}:\radius-\margin-\rd);

\path
({360/4 - 360/\n * (3 - 1)}:{\rer}) edge node [left] {a} ({360/4 - 360/\n * (3 - 1)}:\radius-\margin-\rd);
\path
({360/4 - 360/\n * (4 - 1)}:{\rer}) edge node [left] {a} ({360/4 - 360/\n * (4 - 1)}:\radius-\margin-\rd);
\path
({360/4 + 360/\n * (2 - 1)}:{\rer}) edge node [left] {a} ({360/4 + 360/\n * (2 - 1)}:\radius-\margin-\rd);

\def \alph {360/4 - 360/\n * (5 - 1)}
\foreach \s in {1,...,\N}
{
\path 
({\alph -(360-\alph)/\N *\s}:{\rer}) edge [white,text=black,anchor=south,sloped] node [] {\dots\dots} ({\alph -(360-\alph)/\N *\s}:\radius-\margin-\rd);
}

\path 
({360/4 + 360/\n * (4 - 1)}:{\rer}) edge [white,text=black,anchor=south,sloped] node [] {\dots \dots} ({360/4 + 360/\n * (4 - 1)}:\radius-\margin-\rd);
\end{tikzpicture}
\end{figure}


\end{document}

But it turns out pretty bad – the dots aren't symmetric, and their angle seems to be out of place. Any idea on how I can prettify it?
enter image description here

Thanks!

Best Answer

Following you'll find two options, the first is based in Matsmath suggestion, the second in red is mine. You can choose.

enter image description here

\documentclass{article}
\usepackage{tikz}

\begin{document}

\begin{figure}
\centering
\caption{Star Graph}
\begin{tikzpicture}
\label{star_poa}
\def \n {20}
\def \N {8}
\def \radius {3cm}
\def \rd {1mm}
\def \rer {4mm}

\def \margin {8} % margin in angles, depends on the radius

\node[draw, circle] at (360:0mm) (ustar) {$u_*$};
\foreach \i [count=\ni from 0] in {t,1,2,3,4}{
  \node[draw, circle] at ({108-\ni*18}:\radius) (u\ni) {$u_{\i}$};
  \node at ({115-\ni*18}:\radius/2) {a};
  \draw (ustar)--(u\ni);
}

\foreach \i in {1,3,...,11}{
  \node[circle] at ({-\i*18}:\radius) (aux) {\phantom{$u_{5}$}};
  \draw[dotted, shorten >=3mm, shorten <=3mm] (ustar)--(aux);
}

\draw[dotted,red] (18:\radius/2) arc[start angle=18, end angle=-226, radius=\radius/2];
\end{tikzpicture}
\end{figure}
\end{document}
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