Links in mindmap as table of contents in beamer

Question

I decided to use a mindmap to show the ToC of my presentation and the section outline.

I'd like to have the nodes clickable like the standard ToC, but I couldn't find any command like \insertsection{number_of_section}: \insertsection insert a linked text but only for the current section.

\label/\ref is not a feasible way since:

1. this will go in the code of a theme for (semi)automatic generation
2. beamer is already generating the anchors, so why don't use it?

beamer anchors are named Navigation\c@page, and so I put them manually in the MWE to show roughly what I want to achieve. However, I'd like a sort of automation (by reading \jobname.toc?) since the pages can change.

In addition, is it possible to make the entire circle clickable, and not only the text?

MWE:

\documentclass{beamer}
\usepackage[utf8]{inputenc}
\usepackage{lmodern}\normalfont
\usepackage[T1]{fontenc}
\usepackage{tikz}
\usetikzlibrary{calc,mindmap,trees}
\usepackage{totcount}

\title{There Is No Largest Prime Number\\\small aaa}%
\date[ISPN ?80]{27th International Symposium of Prime Numbers}
\author[Euclid]{Euclid of Alexandria \texttt{euclid@alexandria.edu}}

\tikzset{every mindmap/.style={
                    every node/.style={concept},
                    grow cyclic,
                    concept color=blue!50!green!50!white,
                    text=white,
                    root concept/.style={concept,
                                         fill=white,
                                         line width=1ex,
                                         text=black,
                                         text width=6em,
                                         font=\sffamily\bfseries},
                    level 1 concept/.append style={sibling angle=130/\the\tikznumberofchildren,
                                                   level distance=8cm,
                                                   text width=4em,
                                                   font=\scriptsize\sffamily\bfseries},
                    level 2 concept/.append style={sibling angle=60,
                                                   level distance=5cm,
                                                   font=\scriptsize\sffamily\bfseries},
                    level 3 concept/.append style={sibling angle=50,
%                                                   level distance=2cm,
                                                   font=\scriptsize\sffamily\bfseries}}}


\begin{document}

\begin{frame}{Table of contents}
\centering
\begin{tikzpicture}[small mindmap, scale=0.4, remember picture, overlay]
  \path
    node[root concept] at ($(current page.center) - (3,3)$) {\hyperlink{Navigation1}{There Is No Largest Prime Number}}
    [clockwise from=80]
    child[concept color=blue!70!white] {
      node {\hyperlink{Navigation2}{aaaaa}}
    }
    child[concept color=blue!70!white] {
      node {\hyperlink{Navigation3}{bbbbb}}
      [clockwise from=50]
      child[concept color=orange] {
        node {\hyperlink{Navigation4}{ccccc}}
      }
      child[concept color=orange] {
        node {\hyperlink{Navigation5}{ddddd}}
      }  
    }
    child[concept color=blue!70!white] {
      node {\hyperlink{Navigation6}{eeeee}}
    } ;
\end{tikzpicture}
\end{frame}

\section{aaaaa}
\begin{frame} 
\frametitle{There Is No Largest Prime Number} 
\framesubtitle{The proof uses \textit{reductio ad absurdum}.} 
\begin{theorem}
There is no largest prime number.\end{theorem} 
\begin{enumerate} 
\item Suppose $p$ were the largest prime number. 
\item Let $q$ be the product of the first $p$ numbers. 
\item Then $q+1$ is not divisible by any of them. 
\item But $q + 1$ is greater than $1$, thus divisible by some prime
number not in the first $p$ numbers.
\end{enumerate}
\end{frame}

\section{bbbbb}
\begin{frame}{A longer title}
\begin{itemize}
\item one
\item two
\end{itemize}
\end{frame}

\subsection{ccccc}
\begin{frame}{Void}
\end{frame}

\subsection{ddddd}
\begin{frame}{Void}
\end{frame}

\section{eeee}
\begin{frame}{Void}
\end{frame}

\end{document}

Answer 1

New Version including subsections:

\documentclass{beamer}

\usepackage{tikz}
\usetikzlibrary{mindmap,trees,shadows}

% total number of sections %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\usepackage{totcount}
\newcounter{totalsection}
\regtotcounter{totalsection}

\AtBeginDocument{%
  \pretocmd{\section}{\refstepcounter{totalsection}}{}{}%
}%

% number of subsections per section %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\usepackage{xcntperchap}
\RegisterCounters{section}{subsection}
\newcounter{totalsubsection}
\setcounter{totalsubsection}{0}

% creating automatic label %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% based on https://tex.stackexchange.com/a/386557/36296
\AtBeginSection[]{\label{sec:\thesection}}
\AtBeginSubsection[]{\label{subsec:\thesection:\thesubsection}}
\newcounter{currentsub}
\newcounter{totsection}

\newcommand{\mindtoc}{%
    \centering
    \setcounter{totsection}{\number\totvalue{totalsection}}
  \begin{tikzpicture}[
    grow cyclic,
    concept color=blue!50!black, 
    text=white,
    every node/.style={concept, scale=0.8},
    level 1/.style={%
        sibling angle=360/\thetotsection,
        level distance = 25mm,
        concept color=lime,
        text=black,
    },
    level 2/.style={%
        level distance = 25mm,
        concept color=yellow,
        text=black,
    },      
    ]
        \node {\inserttitle}    [clockwise from=135] child 
        foreach \i in {1,...,\thetotsection}{%
            node{\hyperlink{sec:\i}{\nameref{sec:\i}}
                \setcounter{currentsub}{\ObtainTrackedValueExp[\i]{section}{subsection}}
            }%
            \ifnum\thecurrentsub>0%
                child foreach \j in {1,...,\thecurrentsub}{%
                    node {\hyperlink{subsec:\i:\j}{\nameref{subsec:\i:\j}}} 
                }
            \fi%
        }; 
  \end{tikzpicture}
}

\title{Some Title}

\begin{document}

\begin{frame}
    \frametitle{"Table" of Contents}
    \mindtoc    
\end{frame}

\section{Section One}
\frame{abc}

\section{Section Two}
\frame{abc}

\subsection{subsection a}
\frame{abc}

\subsection{subsection b}
\frame{abc}

\subsection{subsection c}
\frame{abc}

\section{Section Three}
\frame{abc} 

\section{Section Three}
\frame{abc}         

\end{document}

Previous version

The following code automatically generates a toc-map for all sections. Subsections are currently not supported.

\documentclass{beamer}

\usepackage{tikz}
\usetikzlibrary{mindmap,trees,shadows}

\usepackage{etoolbox}
\usepackage{totcount}

\newcounter{totalsection}
\regtotcounter{totalsection}

\setbeamertemplate{section in toc}{\vskip-2.5cm\inserttocsection}

\AtBeginDocument{%
    \pretocmd{\section}{\refstepcounter{totalsection}}{\typeout{Yes, prepending was successful}}{\typeout{No, prepending was not it was successful}}%
}%

\title{Some Title}

\newcommand{\mindtoc}{
    \centering
    \begin{tikzpicture}[mindmap, concept color=blue!50!black, font=\sf, text=white]
        \tikzstyle{level 1 concept}+=[font=\sf, sibling angle=360/\number\totvalue{totalsection},level distance = 33mm]
        \node[concept,scale=0.8] {\inserttitle}
            [clockwise from=135]
            child [concept color=lime] foreach \i in {1,...,\number\totvalue{totalsection}}{
        node[concept,scale=0.8]{\tableofcontents[sections={\i},hidesubsections]}  
            };
    \end{tikzpicture}
}

\begin{document}

\begin{frame}
    \frametitle{"Table" of Contents}
    \mindtoc    
\end{frame}

\section{Section One~}
\frame{abc}

\section{Section Two}
\frame{abc}

\section{Section Three}
\frame{abc} 

\section{Section Three}
\frame{abc}         

\end{document}