hypergraphs

hypergraph_example.tex

\documentclass{minimal}

\usepackage{tikz}
\usepackage{tikz-network}

\usetikzlibrary{calc, backgrounds, positioning}
\input{tikz-hypergraph}

\usepackage{xcolor}

\definecolor{ACMYellow}{RGB}{255, 214, 0}
\definecolor{ACMOrange}{RGB}{252, 146, 0}
\definecolor{ACMRed}{RGB}{253, 27, 20}
\definecolor{ACMLightBlue}{RGB}{131, 206, 226}
\definecolor{ACMGreen}{RGB}{166, 188, 9}
\definecolor{ACMPurple}{RGB}{101, 1, 107}
\definecolor{ACMDarkBlue}{RGB}{9, 53, 122}


\begin{document}
	
\begin{tikzpicture}
\tikzstyle{important}=[draw, circle, minimum size=8mm, fill=white];
\tikzstyle{unimportant}=[draw, circle, minimum size=4mm, fill=white];

\node at (0,1) (v1) {};
\node at (2,1.75) (v2) {};
\node at (2,0) (v3) {};
\node at (4,3) (v4) {};
\node at (4,0) (v5) {};
\node at (6,1) (v6) {};
\node at (4.55,-1.5) (v7) {};
\node at (0.75,2) (v8) {};
\node at (2.5,3.5) (v9) {};

\draw[draw, fill=ACMDarkBlue, fill opacity=0.5] \hedgem{v1}{v8}{v2,v3}{6mm};
\draw[draw, fill=ACMRed, fill opacity=0.5] \hedgem{v2}{v9}{v4}{6mm};
\draw[draw, fill=ACMPurple, fill opacity=0.5] \hedgem{v5}{v4}{v6}{6mm};
\draw[draw, fill=ACMOrange, fill opacity=0.5] \hedgem{v3}{v6}{v7}{6mm};

\node[important] at (v1) {$v_1$};
\node[important] at (v2) {$v_2$};
\node[important] at (v3) {$v_3$};
\node[important] at (v4) {$v_4$};
\node[important] at (v5) {$v_5$};
\node[important] at (v6) {$v_6$};
\node[unimportant] at (v7) {};
\node[unimportant] at (v8) {};
\node[unimportant] at (v9) {};

\node at (1, 1) {$e_1$};
\node at (2.75, 2.75) {$e_2$};
\node at (3.5, -1) {$e_3$};
\node at (4.75, 2) {$e_4$};

\end{tikzpicture}

\end{document}

tikz-hypergraph.tex

% Needs
% \usetikzlibrary{calc}
% \usepackage{ifthen}

\def\rotateclockwise#1{
  % Rotate input point by 90 degrees clockwise.
  \newdimen\xrw
  \pgfextractx{\xrw}{#1}
  \newdimen\yrw
  \pgfextracty{\yrw}{#1}
  % \pgfpoint{-\y}{\x}
  \pgfpoint{\yrw}{-\xrw}
}

\def\rotatecounterclockwise#1{
  % Rotate input point by 90 degrees clockwise.
  \newdimen\xrcw
  \pgfextractx{\xrcw}{#1}
  \newdimen\yrcw
  \pgfextracty{\yrcw}{#1}
  % \pgfpoint{-\y}{\x}
  \pgfpoint{-\yrcw}{\xrcw}
}

\def\outsidespacerpgfclockwise#1#2#3{
  % #1 start point
  % #2 end point
  % #3 radius
  % Compute a length-radius vector perpendicular (clockwise)
  % to the vector from start point to end point.
  \pgfpointscale{#3}{
    \rotateclockwise{
      \pgfpointnormalised{
        \pgfpointdiff{#1}{#2}}}}
}

\def\outsidespacerpgfcounterclockwise#1#2#3{
  % #1 start point
  % #2 end point
  % #3 radius
  % Compute a length-radius vector perpendicular (counterclockwise)
  % to the line from start point to end point.
  \pgfpointscale{#3}{
    \rotatecounterclockwise{
      \pgfpointnormalised{
        \pgfpointdiff{#1}{#2}}}}
}

\def\outsidepgfclockwise#1#2#3{
  % #1 start point
  % #2 end point
  % #3 radius
  % Add to end point a length-radius vector perpendicular
  % (counter-clockwise) to the line from start point to end point.
  \pgfpointadd{#2}{\outsidespacerpgfclockwise{#1}{#2}{#3}}
}

\def\outsidepgfcounterclockwise#1#2#3{
  % #1 start point
  % #2 end point
  % #3 radius
  % Add to end point a length-radius vector perpendicular
  % (counter-clockwise) to the line from start point to end point.
  \pgfpointadd{#2}{\outsidespacerpgfcounterclockwise{#1}{#2}{#3}}
}

\def\outside#1#2#3{
  ($ (#2) ! #3 ! -90 : (#1) $)
}

\def\cornerpgf#1#2#3#4{
  % #1 = previous pgf point 
  % #2 = current pgf point
  % #3 = next pgf point
  % #4 = radius
  % Computes a path comprising a rounded corner on the outside of the angle #1#2#3.
  \pgfextra{
    \pgfmathanglebetweenpoints{#2}{\outsidepgfcounterclockwise{#1}{#2}{#4}}
    \let\anglea\pgfmathresult
    \let\startangle\pgfmathresult

    \pgfmathanglebetweenpoints{#2}{\outsidepgfclockwise{#3}{#2}{#4}}
    \pgfmathparse{\pgfmathresult - \anglea}
    \pgfmathroundto{\pgfmathresult}
    \let\arcangle\pgfmathresult
    \ifthenelse{180=\arcangle \or 180<\arcangle}{
      \pgfmathparse{-360 + \arcangle}}{
      \pgfmathparse{\arcangle}}
    \let\deltaangle\pgfmathresult

    \newdimen\x
    \pgfextractx{\x}{\outsidepgfcounterclockwise{#1}{#2}{#4}}
    \newdimen\y
    \pgfextracty{\y}{\outsidepgfcounterclockwise{#1}{#2}{#4}}
  }
  -- (\x,\y) arc [start angle=\startangle, delta angle=\deltaangle, radius=#4]
}

\def\corner#1#2#3#4{
  \cornerpgf{\pgfpointanchor{#1}{center}}{\pgfpointanchor{#2}{center}}{\pgfpointanchor{#3}{center}}{#4}
}


\def\hedgeiii#1#2#3#4{
  % #1#2#3 = tikz points
  % #4 = radius
  % Computes a path comprising the line of the points outside of the
  % convex hull H of the points #1#2#3 that have distance #4 to H.
  % Points #1#2#3 need to be in clockwise order.
  \outside{#1}{#2}{#4} \corner{#1}{#2}{#3}{#4} \corner{#2}{#3}{#1}{#4} \corner{#3}{#1}{#2}{#4} -- cycle
}

\def\hedgem#1#2#3#4{
  % #1#2 = tikz points
  % #3 = list of tikz points
  % #4 = radius
  % Computes a path comprising the line of the points outside of the convex hull H of the points #1#2[#3] that have distance #4 to H.
  % Points #1#2[#3] need to be vertices of a convex polygon and in clockwise order.
  
  \outside{#1}{#2}{#4}
  \pgfextra{
    \def\hgnodea{#1}
    \def\hgnodeb{#2}
  }
  foreach \c in {#3} {
    \corner{\hgnodea}{\hgnodeb}{\c}{#4}
    \pgfextra{
      \global\let\hgnodea\hgnodeb
      \global\let\hgnodeb\c
    }
  }
  \corner{\hgnodea}{\hgnodeb}{#1}{#4}
  \corner{\hgnodeb}{#1}{#2}{#4}
  -- cycle
}

\def\hedgeii#1#2#3{
  % #1#2 = tikz points
  % #3 = radius
  \hedgem{#1}{#2}{}{#3}
}

\def\hedgei#1#2{
  % #1 = tikz point
  % #2 = radius
  (#1) circle [radius = #2]
}