Plot directed graph from transition matrix in tikz

graphstikz-arrowstikz-pgf

I would like to plot a directed graph in tikz starting from a transition matrix as the one below. A "1" in position ij indicates state i leads to state j.

[0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0;
 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0;
 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0;
 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0;
 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0;
 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0;
 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0;
 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0;
 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0]

Starting from this (or something similar), I would like to automatically generate a directed graph in tikz. Can you point me in the right direction on how to achieve this?

EDIT: Ideally, I would like the nodes to be located similarly to this https://r-graphics.org/R-Graphics-Cookbook-2e_files/figure-html/FIG-MISCGRAPH-GRAPH-DIRECTED-1.png

Best Answer

Perhaps this could be a start point? I don't know where to put the nodes so I'm not sure. Anyway, this is my idea:

\documentclass[tikz,border=2mm]{standalone}
\tikzset{my node/.style={draw,circle,minimum size=0.75cm}}

\begin{document}
\begin{tikzpicture}
\def\nn{5} % number of nodes
\def\r{3}  % radius
\foreach\i in {1,...,\nn}
  \node[draw,circle] (\i) at ({360/\nn*(\i-1)}:\r) {\i};
\foreach[count=\j]\i in {% Matrix:
1,1,1,0,0,
0,1,0,0,1,
1,1,0,1,1,
0,0,0,1,0,
1,0,0,1,0
}
{
  \ifnum\i=1
    \pgfmathtruncatemacro\row{div(\j-1,\nn)+1}
    \pgfmathtruncatemacro\col{mod(\j-1,\nn)+1}
    \ifnum\row=\col% same initial and final state
      \pgfmathtruncatemacro\a{360/\nn*(\row-1)+30}
      \pgfmathtruncatemacro\b{\a-60}
      \draw[->] (\row.\a) to[out=\a,in=\b,looseness=4] (\row.\b);
    \else
      \draw[->] (\row) -- (\col);
    \fi
  \fi
}
\end{tikzpicture}
\end{document}

And the output:

Related Solutions

[Tex/LaTex] Simple directed hypergraphs in TikZ

A second attempt, this time making some assumptions on the layout. I assume you want the hyper-edge to always be aligned to the "lonely" node of the triplets (e.g. c in ({a,b},{c}) and ({c},{a,b}) ).

Since you seem to need fine control on the positioning of the nodes I suggest the following: first you place named nodes with manual positioning (using whichever method you prefer, from absolute coordinates to relative positioning); then you specify the hyperedges and the corresponding arcs get created. Here's a macro that can help you with the second step:

\newcommand{\hyperedge}[4][180]{
     \draw (#2.#1) ++(#1:.5)  edge (#2) edge (#3) edge (#4);
}

It takes 4 arguments (first optional): \hyperedge[angle]{c}{a}{b} draws the edges assuming that c is the lonely node and requires you to specify the angle at which the hyperedge should stick out of it.

The definition of the macro works by moving to the right/left border of the lonely node (this is accomplished by (#2.#1) which moves to the border of the node #2 at angle #1), then move right/left by .5 which is the coordinate of the "centre" of the edge; then this "centre" is connected with the nodes using the edge action.

Here's your second example using tikz and my macro:

\documentclass{standalone}
\usepackage{tikz}

\newcommand{\hyperedge}[4][180]{
     \draw (#2.#1) ++(#1:.5)  edge (#2) edge (#3) edge (#4);    
}

\begin{document}
\begin{tikzpicture}[
    y=.7cm, x=1cm,
    every edge/.append style={thick}
]

\node (a) at (-1,1) {a};
\node (b) at (-1,-1) {b};
\node (c) at (0,0) {c};
\node (d) at (1,1) {d};
\node (e) at (1,-1) {e};
\node (g) at (2,-2) {g};

\hyperedge{c}{b}{a}
\hyperedge[0]{c}{d}{e}
\hyperedge{g}{b}{e}


\end{tikzpicture}

\end{document}

Which is rather readable and easy to extend.

You can elaborate on this by using other means to specify the angle (other derived macros) or enriching it with custom styles.

Another option for the placement of the "centre" of the hyperedge is barycentric coordinates:

\newcommand{\hyperedge}[3]{
    \draw (barycentric cs:#1=1,#2=1,#3=1) edge (#1) edge (#2) edge (#3);
}

Note that this does not require the angle argument.

[Tex/LaTex] How to produce this Matlab social network graph from an adjacency matrix in Tikz

A bit crude, but sort of works OK and requires lualatex. A simple parser (which just matches on non-whitespace) plus a graph drawing macro.

\RequirePackage{luatex85}
\documentclass[tikz,border=5]{standalone}
\usetikzlibrary{graphs,graphdrawing}
\usegdlibrary{force,trees}
\usepackage{luacode}
\begin{luacode*}
function parseNetwork(nodeWeights, adjacencyMatrix)
  local i, j, n, v, w, str
  n = 0
  weights = {}
  for str in string.gmatch(nodeWeights, "[^%s]+") do
    w = tonumber(str)
        tex.print("n" .. n + 1 .. "/[minimum size=" .. w .. ", label=center:node" .. n  + 1 .. "];")
      n = n + 1
  end
  i = 0
  j = 0
  for str in string.gmatch(adjacencyMatrix, "[^%s]+") do
    v = tonumber(str)
      if v > 0 then
        if j > i then
        tex.print("n" .. i + 1 ..  " --[line width=" .. (v / 100) .. "]" .. "n" .. j + 1 .. ";")
        end
      end
        j = (j + 1) % n
        if j == 0 then i = i + 1 end
  end
end
\end{luacode*}
\tikzgraphsset{%
  node weights/.store in=\nodeweights,
  adjacency matrix/.store in=\adjacencymatrix,
  declare={network}{
  [/utils/exec={%
    \edef\networkspec{\directlua{parseNetwork("\nodeweights","\adjacencymatrix")}}},
    parse/.expanded=\networkspec] 
}}
\begin{document}
\begin{tikzpicture}
\graph [spring electrical layout, 
  edges={draw=blue!50!cyan, shorten >=-1em, shorten <=-1em}, 
  nodes={circle, fill=blue!50!cyan!50},
  electric charge=10]{
    network [
      node weights={
    56    42    39    34    32    31    30    29    28    28
    },
      adjacency matrix={
     0   741   630   406   325   325   351     0   300   276
   741     0   406   351   276     0     0     0     0     0
   630   406     0   300     0   276   300     0     0     0
   406   351   300     0     0     0     0     0     0     0
   325   276     0     0     0     0     0     0     0     0
   325     0   276     0     0     0   276     0     0     0
   351     0   300     0     0   276     0     0     0     0
     0     0     0     0     0     0     0     0     0     0
   300     0     0     0     0     0     0     0     0     0
   276     0     0     0     0     0     0     0     0     0
}]; 
};
\end{tikzpicture}
\end{document}

Best Answer

Related Solutions

[Tex/LaTex] Simple directed hypergraphs in TikZ

[Tex/LaTex] How to produce this Matlab social network graph from an adjacency matrix in Tikz

Related Question