Graph Properties / Features

13. Two graphs are isomorphic if there exists a one-to-one correspondence between their vertices that preserves adjacency.
    
    In other words, two isomorphic graphs have the same structure even if their drawings or vertex labels are different.
    

    Two isomorphic graphs: just move the vertices around to turn the left graph into the right one. Miriam Briskman, CC BY-NC 4.0.

    \documentclass[border=1pt]{standalone}
    \usepackage{tikz}
    
    \tikzset{
    vertex/.style={draw, circle, very thick, minimum size=1cm},
    edge/.style={very thick}
    }
    
    \begin{document}
    
    \begin{tikzpicture}
    
    % First graph
    \node[vertex] (v1) at (0,0) {$1$};
    \node[vertex] (v2) at (3,1) {$2$};
    \node[vertex] (v3) at (1.85,-0.6) {$3$};
    \node[vertex] (v4) at (2.4,-2) {$4$};
    
    \draw[edge] (v1) -- (v2);
    \draw[edge] (v1) -- (v3);
    \draw[edge] (v2) -- (v3);
    \draw[edge] (v2) -- (v4);
    \draw[edge] (v1) -- (v4);
    \draw[edge] (v3) -- (v4);
    
    \draw (4.5, 1.5) -- (4.5, -2.5);
    
    % Second graph
    \node[vertex] (v5) at (6,1) {$1$};
    \node[vertex] (v6) at (9,1) {$2$};
    \node[vertex] (v7) at (6,-2) {$3$};
    \node[vertex] (v8) at (9,-2) {$4$};
    
    \draw[edge] (v5) -- (v6);
    \draw[edge] (v5) -- (v7);
    \draw[edge] (v6) -- (v7);
    \draw[edge] (v6) -- (v8);
    \draw[edge] (v5) -- (v8);
    \draw[edge] (v7) -- (v8);
    
    \end{tikzpicture}
    
    \end{document}