stargraph.tex

\documentclass{article}
\usepackage{tikz}

\tikzset{
  star graph/.pic={
    \node[
        fill,
        inner sep=0pt,
        outer sep=0pt,
        circle,
        minimum size=\pgfkeysvalueof{/tikz/star graph/vertex size},
        node contents={},
        at={(0,0)},
        name=centre,
        star graph/every vertex/.try,
        star graph/centre/.try,
    ];
    \foreach \n in {1,...,#1} {
      \node[
        fill,
        inner sep=0pt,
        outer sep=0pt,
        circle,
        minimum size=\pgfkeysvalueof{/tikz/star graph/vertex size},
        node contents={},
        at={({\n*360/#1 + \pgfkeysvalueof{/tikz/star graph/start angle}}:\pgfkeysvalueof{/tikz/star graph/edge size})},
        name=vertex \n,
        star graph/every vertex/.try=\n,
        star graph/vertex \n/.try=\n
      ];
      \draw[
        star graph/every edge/.try=\n,
        star graph/edge \n/.try=\n
      ] (centre) -- (vertex \n);
    }
  },
  star graph/.is family,
  star graph/.cd,
  vertex size/.initial=10pt,
  edge size/.initial=3cm,
  start angle/.initial=0
}

\begin{document}
\begin{tikzpicture}
\pic[
  star graph/.cd,
  every edge/.style={
    red,
    ultra thick,
  },
  every vertex/.style={
    blue,
    label={#1}
  },
  centre/.style={
    purple
  },
  start angle=30
] {star graph=5};
\end{tikzpicture}

\end{document}