Αρχείο:Non transitive relation example graph and matrix.svg

\documentclass[border=3mm, tikz]{standalone}

\usepackage{pgfplots}
\usepackage{xcolor}

\usepackage[utf8x]{inputenc}
\usepackage[greek,english]{babel}

\definecolor{Red}{HTML}{ff7979}
\definecolor{Green}{HTML}{8ac478}
\definecolor{Blue}{HTML}{80bfff}

\usepackage{tabularray}

\begin{document}
\begin{tikzpicture}
\tikzset{nd/.style={circle,thick,fill=black,minimum size=0.5mm,scale=0.35}}
\tikzset{arr/.style={-{>[width=1mm,length=0.8mm]}}}
\tikzset{Marked/.style={draw=red,dash pattern={on 0.35mm off 0.35mm}}}

% The positions of the nodes.
\node[nd] (a1) at (0, 0) {};
\node[nd] (a2) at (1.2, 0) {};
\node[nd] (a4) at (0, -0.8) {};
\node[nd] (a3) at (1.2, -0.8) {};
\node[nd] (a5) at (0, -1.6) {};
\node[nd] (a6) at (1.2, -1.6) {};

% The edges in the relation.
\path[Marked, arr] (a1) edge (a3);
\path[arr] (a1) edge (a4);
\path[Marked, arr] (a1) edge[bend right=30] (a5);

\path[arr] (a2) edge (a3);
\path[arr,Marked] (a2) edge (a4);
\path[arr,Marked] (a2) edge (a5);

\path[arr] (a3) edge[bend left=15] (a5);

\path[arr] (a3) edge[bend left=15] (a4);
\path[arr] (a4) edge[bend left=15] (a3);
\path[arr,Marked] (a4) edge (a5);

% \path[arr] (a6) edge[bend left=15] (a5);

% The self-loops of the relations.
\path[Marked,->] (a3) edge[in=40,out=-20,loop,looseness=8] (a3);
\path[Marked,->] (a4) edge[in=180,out=120,loop,looseness=8] (a4);


% The labels of the nodes.
\node[anchor=south east,scale=0.5] at (a1) {$1$};
\node[anchor=south west,scale=0.5,xshift=0.2cm] at (a2) {$2$};
\node[anchor=north west,scale=0.5,xshift=0.3cm] at (a3) {$3$};
\node[anchor=north east,scale=0.5] at (a4) {$4$};
\node[anchor=north,scale=0.5,yshift=-0.1cm] at (a5) {$5$};
\node[anchor=north,scale=0.5,yshift=-0.1cm] at (a6) {$6$};

% The matrix representation of the relation.
\node[scale=0.4] at (2.75, -0.8) {
$M(R) = \quad $\begin{tblr}{
  rows = {1.5em, rowsep = 2pt},
  columns = {1.5em, colsep = 2pt},
  cells = {m,c},
  hlines = {1pt},
  vlines = {1pt},
  cell{1}{3} = {Red},
  cell{1}{4} = {Green},
  cell{1}{5} = {Red},
  cell{2}{3} = {Green},
  cell{2}{4} = {Red},
  cell{2}{5} = {Red},
  cell{3}{3} = {Red},
  cell{3}{4} = {Green},
  cell{3}{5} = {Green},
  cell{4}{3} = {Green},
  cell{4}{4} = {Red},
  cell{4}{5} = {Red},
}
0 & 0 & 0 & 1 & 0 & 0 \\
0 & 0 & 1 & 0 & 0 & 0 \\ 
0 & 0 & 0 & 1 & 1 & 0 \\ 
0 & 0 & 1 & 0 & 0 & 0 \\ 
0 & 0 & 0 & 0 & 0 & 0 \\ 
0 & 0 & 0 & 0 & 0 & 0 \\
\end{tblr}
};

\end{tikzpicture}
\end{document}