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Here are some isomorphic graphs and their corresponding adjacency matrices. I can draw the graphs with tikz. But I'm not sure the best way to draw the matrices. Is it possible to generate one from the other? What's the right way to approach it?

Here's an example of the code to generate a graph:

 documentclass{standalone}

usepackage{tikz}

begin{document}

begin{tikzpicture}

tikzset{Bullet/.style={circle,draw,fill=black,scale=0.75}}

node[Bullet,label=left :{$e_1$}] (E1) at (0,2) {} ;

node[Bullet,label=above:{$e_2$}] (E2) at (1,3) {} ;

node[Bullet,label=right:{$e_3$}] (E3) at (2,2) {} ;

node[Bullet,label=right:{$e_4$}] (E4) at (2,0) {} ;

node[Bullet,label=left :{$e_5$}] (E5) at (0,0) {} ;

draw[thick] (E1)--(E2)--(E3)--(E4)--(E5)--(E1) {} ;

end{tikzpicture}

end{document}

This is in case you change your mind and use the adjacency matrices to draw the graphs. TikZ allows you to define arrays, see p. 999 of the pgfmanual. And these arrays can be converted to tables using this nice answer. And these matrices/arrays can also be used to define the graphs.

documentclass[tikz,border=3.14mm]{standalone}

usepackage{etoolbox}

usetikzlibrary{matrix,positioning}

% building the table in a foreach loop from https://tex.stackexchange.com/a/60400/121799

begin{document}

begin{tikzpicture}[Bullet/.style={circle,draw,fill=black,inner sep=1.5pt},

adjacency matrix/.style={ampersand replacement=&,matrix of math nodes,

 row 1/.append style={nodes={font=boldmath}},

 column 1/.append style={nodes={font=boldmath}},nodes in empty cells,

nodes={draw,minimum width=1.5em,text height=1.8ex},column sep=-pgflinewidth,row

sep=-pgflinewidth}]

% first matrix

defadjancymatrix{%

{{0,0,1,1,0},%

{0,0,0,1,1},%

{1,0,0,0,1},%

{1,1,0,0,0},%

{0,1,1,0,0}}} 

 letmymatrixcontentempty

 defmymatrixcontent{|[draw=none]|& 1 & 2 & 3 & 4  & 5\}

 begin{scope}[local bounding box=left]

  foreach X in {1,...,5}

   {node[Bullet,label=90+72-X*72:{$e_X$}] (EX) at (90+72-X*72:2) {} ;}

  foreach X in {1,...,5}

  {begingroupedefx{endgroup

         noexpandgapptonoexpandmymatrixcontent{X }}x

  foreach Y in {1,...,5}

   {pgfmathtruncatemacro{itest}{adjancymatrix[X-1][Y-1]}

   ifnumitest=1

    draw (EX) -- (EY);

    begingroupedefx{endgroup

         noexpandgapptonoexpandmymatrixcontent{& 1 }}x

   else

    begingroupedefx{endgroup

         noexpandgapptonoexpandmymatrixcontent{ &}}x

   fi

   }

   gapptomymatrixcontent{\}

   }

 end{scope} 

 matrix (leftmat) [below=of left,adjacency matrix]{

    mymatrixcontent

  };

 %

% second matrix

defadjancymatrix{%

{{0,1,0,0,1},%

{1,0,1,0,0},%

{0,1,0,1,0},%

{0,0,1,0,1},%

{1,0,0,1,0}}} 

 letmymatrixcontentempty

 defmymatrixcontent{|[draw=none]|& 1 & 2 & 3 & 4  & 5\}

 begin{scope}[local bounding box=middle,xshift=5cm]

  foreach X in {1,...,5}

   {node[Bullet,label=90+72-X*72:{$e_X$}] (EX) at (90+72-X*72:2) {} ;}

  foreach X in {1,...,5}

  {begingroupedefx{endgroup

         noexpandgapptonoexpandmymatrixcontent{X }}x

  foreach Y in {1,...,5}

   {pgfmathtruncatemacro{itest}{adjancymatrix[X-1][Y-1]}

   ifnumitest=1

    draw (EX) -- (EY);

    begingroupedefx{endgroup

         noexpandgapptonoexpandmymatrixcontent{& 1 }}x

   else

    begingroupedefx{endgroup

         noexpandgapptonoexpandmymatrixcontent{ &}}x

   fi

   }

   gapptomymatrixcontent{\}

   }

 end{scope} 

 matrix (midmat) [below=of middle,adjacency matrix]{

    mymatrixcontent

  };

% third matrix

defadjancymatrix{%

{{0,1,0,1,0},%

{1,0,0,0,1},%

{0,0,0,1,1},%

{1,0,1,0,0},%

{0,1,1,0,0}}} 

 letmymatrixcontentempty

 defmymatrixcontent{|[draw=none]|& 1 & 2 & 3 & 4  & 5\}

 begin{scope}[local bounding box=right,xshift=10cm]

  foreach X in {1,...,3}

   {node[Bullet,label=90+72-X*72:{$e_X$}] (EX) at (90+72-X*72:2) {} ;}

  node[Bullet,label=90+72-4*72:{$e_5$}] (E5) at (90+72-4*72:2) {} ; 

  node[Bullet,label=90+72-5*72:{$e_4$}] (E4) at (90+72-5*72:2) {} ; 

  foreach X in {1,...,5}

  {begingroupedefx{endgroup

         noexpandgapptonoexpandmymatrixcontent{X }}x

  foreach Y in {1,...,5}

   {pgfmathtruncatemacro{itest}{adjancymatrix[X-1][Y-1]}

   ifnumitest=1

    draw (EX) -- (EY);

    begingroupedefx{endgroup

         noexpandgapptonoexpandmymatrixcontent{& 1 }}x

   else

    begingroupedefx{endgroup

         noexpandgapptonoexpandmymatrixcontent{ &}}x

   fi

   }

   gapptomymatrixcontent{\}

   }

 end{scope} 

 matrix (rightmat) [below=of right,adjacency matrix]{

    mymatrixcontent

  };



end{tikzpicture}

end{document}