Graphs can look differently but be identical. The only thing that matters are which nodes are connected to which other nodes. If there exists an edge-preserving bijection between two graphs, in other words if there exists a function that maps nodes from one graph onto those of another such that the set of connections for each node remain identical, the two graph are said to be isomorphic.

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% Graphs can look differently but be identical. The only thing that matters are which % nodes are connected to which other nodes. If there exists an edge-preserving bijection % between two graphs, in other words if there exists a function that maps nodes from one % graph onto those of another such that the set of connections for each node remain identical, % the two graph are said to be isomorphic. \documentclass[tikz]{standalone} \begin{document} \begin{tikzpicture}[ vertex/.style = {circle, draw, inner sep=1pt, fill=white}, vertex1/.style = {vertex, fill=red!30!white}, vertex2/.style = {vertex, fill=orange!30!white}, vertex3/.style = {vertex, fill=blue!30!white}, vertex4/.style = {vertex, fill=teal!30!white}, ] \draw[thick] (0,0) node[vertex1] (n1^1) {$n_1$} -- (0,2) node[vertex2] (n2^1) {$n_2$} -- (2,2) node[vertex3] (n3^1) {$n_3$} -- (2,0) node[vertex4] (n4^1) {$n_4$} -- cycle; \begin{scope}[xshift=4cm] \draw[thick] (0,0) node[vertex1] (n1^2) {$n_1$} -- (2,2) node[vertex2] (n2^2) {$n_2$} -- (0,2) node[vertex3] (n3^2) {$n_3$} -- (2,0) node[vertex4] (n4^2) {$n_4$} -- cycle; \end{scope} \begin{scope}[xshift=8cm] \draw[thick] (0,0) node[vertex1] (n1^3) {$n_1$} -- (2,2) node[vertex2] (n2^3) {$n_2$} -- (2,0) node[vertex4] (n3^3) {$n_3$} -- (0,2) node[vertex3] (n4^3) {$n_4$} -- cycle; \end{scope} \begin{scope}[xshift=12.5cm] \draw[thick] (-0.5,0) node[vertex1] (n1^4) {$n_1$} -- (0.25,2.2) node[vertex2] (n2^4) {$n_2$} -- (2,1.6) node[vertex3] (n3^4) {$n_3$} -- (-0.7,1.4) node[vertex4] (n4^4) {$n_4$} -- cycle; \end{scope} \end{tikzpicture} \end{document}

Click to download: graph-isomorphism.tex

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This file is available on tikz.netlify.app and on GitHub and is MIT licensed.

See more on the author page of Janosh Riebesell..