Generating adjacency matrices from isomorphic graphs












5















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?



enter image description here



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}









share|improve this question

























  • Shouldn't it be the other way around: you construct the diagrams from the adjacency matrices?

    – marmot
    yesterday











  • @marmot Probably, normally. Actually I don't think so. I mean.. Either way is probably good. But I have some graphs drawn up, and I want to draw the matrices to suit them. If I can't figure it out programmatically, I'll just draw them up separately. Either with LaTeX somehow or with Adobe Illustrator, or some spreadsheet/word processor. LaTeX would be nice though.

    – tjt263
    yesterday






  • 1





    Your graphics would be more informative if you did not shuffle vertex locations around between (a), (b) and (c).

    – Szabolcs
    yesterday











  • @Szabolcs that's exactly what I've done. Just need to draw the adjacency matrix. The image I posted was just a screenshot I had on my phone. But I've drawn them like you say. The vertices and labels stay the same, and the edges change.

    – tjt263
    yesterday
















5















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?



enter image description here



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}









share|improve this question

























  • Shouldn't it be the other way around: you construct the diagrams from the adjacency matrices?

    – marmot
    yesterday











  • @marmot Probably, normally. Actually I don't think so. I mean.. Either way is probably good. But I have some graphs drawn up, and I want to draw the matrices to suit them. If I can't figure it out programmatically, I'll just draw them up separately. Either with LaTeX somehow or with Adobe Illustrator, or some spreadsheet/word processor. LaTeX would be nice though.

    – tjt263
    yesterday






  • 1





    Your graphics would be more informative if you did not shuffle vertex locations around between (a), (b) and (c).

    – Szabolcs
    yesterday











  • @Szabolcs that's exactly what I've done. Just need to draw the adjacency matrix. The image I posted was just a screenshot I had on my phone. But I've drawn them like you say. The vertices and labels stay the same, and the edges change.

    – tjt263
    yesterday














5












5








5


1






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?



enter image description here



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}









share|improve this question
















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?



enter image description here



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}






diagrams matrices graphs tikz-pic






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share|improve this question













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edited yesterday







tjt263

















asked yesterday









tjt263tjt263

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  • Shouldn't it be the other way around: you construct the diagrams from the adjacency matrices?

    – marmot
    yesterday











  • @marmot Probably, normally. Actually I don't think so. I mean.. Either way is probably good. But I have some graphs drawn up, and I want to draw the matrices to suit them. If I can't figure it out programmatically, I'll just draw them up separately. Either with LaTeX somehow or with Adobe Illustrator, or some spreadsheet/word processor. LaTeX would be nice though.

    – tjt263
    yesterday






  • 1





    Your graphics would be more informative if you did not shuffle vertex locations around between (a), (b) and (c).

    – Szabolcs
    yesterday











  • @Szabolcs that's exactly what I've done. Just need to draw the adjacency matrix. The image I posted was just a screenshot I had on my phone. But I've drawn them like you say. The vertices and labels stay the same, and the edges change.

    – tjt263
    yesterday



















  • Shouldn't it be the other way around: you construct the diagrams from the adjacency matrices?

    – marmot
    yesterday











  • @marmot Probably, normally. Actually I don't think so. I mean.. Either way is probably good. But I have some graphs drawn up, and I want to draw the matrices to suit them. If I can't figure it out programmatically, I'll just draw them up separately. Either with LaTeX somehow or with Adobe Illustrator, or some spreadsheet/word processor. LaTeX would be nice though.

    – tjt263
    yesterday






  • 1





    Your graphics would be more informative if you did not shuffle vertex locations around between (a), (b) and (c).

    – Szabolcs
    yesterday











  • @Szabolcs that's exactly what I've done. Just need to draw the adjacency matrix. The image I posted was just a screenshot I had on my phone. But I've drawn them like you say. The vertices and labels stay the same, and the edges change.

    – tjt263
    yesterday

















Shouldn't it be the other way around: you construct the diagrams from the adjacency matrices?

– marmot
yesterday





Shouldn't it be the other way around: you construct the diagrams from the adjacency matrices?

– marmot
yesterday













@marmot Probably, normally. Actually I don't think so. I mean.. Either way is probably good. But I have some graphs drawn up, and I want to draw the matrices to suit them. If I can't figure it out programmatically, I'll just draw them up separately. Either with LaTeX somehow or with Adobe Illustrator, or some spreadsheet/word processor. LaTeX would be nice though.

– tjt263
yesterday





@marmot Probably, normally. Actually I don't think so. I mean.. Either way is probably good. But I have some graphs drawn up, and I want to draw the matrices to suit them. If I can't figure it out programmatically, I'll just draw them up separately. Either with LaTeX somehow or with Adobe Illustrator, or some spreadsheet/word processor. LaTeX would be nice though.

– tjt263
yesterday




1




1





Your graphics would be more informative if you did not shuffle vertex locations around between (a), (b) and (c).

– Szabolcs
yesterday





Your graphics would be more informative if you did not shuffle vertex locations around between (a), (b) and (c).

– Szabolcs
yesterday













@Szabolcs that's exactly what I've done. Just need to draw the adjacency matrix. The image I posted was just a screenshot I had on my phone. But I've drawn them like you say. The vertices and labels stay the same, and the edges change.

– tjt263
yesterday





@Szabolcs that's exactly what I've done. Just need to draw the adjacency matrix. The image I posted was just a screenshot I had on my phone. But I've drawn them like you say. The vertices and labels stay the same, and the edges change.

– tjt263
yesterday










2 Answers
2






active

oldest

votes


















6














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}


enter image description here






share|improve this answer


























  • Not bad, can we get the matrix lines drawn in or is it just like that

    – tjt263
    yesterday











  • @tjt263 Yes, sure.

    – marmot
    yesterday











  • Excellent. Wish I could go the other way. Maybe I will just try to draw them manually instead.

    – tjt263
    yesterday











  • What package can I draw them with manually? I like exactly how yours look.

    – tjt263
    23 hours ago













  • @tjt263 Sorry, I do not understand your question (because I do not know what "manually" means), nor your concerns. In order to draw these graphs, you need to know how they should look. The adjacency matrices have an almost minimal set of information. What kind of minimal set of information are you proposing to define the graphs?

    – marmot
    18 hours ago



















2














Here is a sagetex solution which uses the computer algebra system, SAGE, to do the work. SAGE has built in knowledge of different classes of graphs and has some compatibility with LaTeX and Tikz and can solve some graph parameters as well. All that knowledge means SAGE is not part of the LaTeX distribution, but this is easily handled with a free Cocalc account. It might be my lack of knowledge about the subject but I had trouble trying to get the graphs to look exactly the way you have drawn them but if you're willing to give up some control here is a straightforward implementation of what you want.



documentclass{article}
usepackage{sagetex}
usepackage{tikz,tkz-graph,tkz-berge}
begin{document}
begin{sagesilent}
H = Graph({1:[2], 2:[3], 3:[4], 4:[5], 5:[1]})
H.set_pos(H.layout_circular()) #arrange the vertices in a circle
H.set_latex_options(scale=1.0,graphic_size=(3,3))
######
J = Graph({1:[2], 2:[5], 3:[4], 4:[1], 5:[3]})
J.set_pos(H.layout_circular()) #arrange the vertices in a circle
J.set_latex_options(scale=1.0,graphic_size=(3,3))
######
K = Graph({1:[3], 2:[4], 3:[5], 4:[1], 5:[2]})
K.set_pos(H.layout_circular()) #arrange the vertices in a circle
K.set_latex_options(scale=1.0,graphic_size=(3,3))
end{sagesilent}
Consider the three graphs below:\\

begin{tabular}{ccc}
begin{tikzpicture}
GraphInit[vstyle=Normal]
SetVertexNormal[Shape=circle,LineWidth = 1pt]
tikzset{EdgeStyle/.append style = {color = black, line width=1pt}}
sage{H}
end{tikzpicture} &
begin{tikzpicture}
GraphInit[vstyle=Normal]
SetVertexNormal[Shape=circle,LineWidth = 1pt]
tikzset{EdgeStyle/.append style = {color = black, line width=1pt}}
sage{J}
end{tikzpicture} &
begin{tikzpicture}
GraphInit[vstyle=Normal]
SetVertexNormal[Shape=circle,LineWidth = 1pt]
tikzset{EdgeStyle/.append style = {color = black, line width=1pt}}
sage{K}
end{tikzpicture}\
$sage{H.adjacency_matrix()}$ & $sage{J.adjacency_matrix()}$ & $sage{K.adjacency_matrix()}$\\
(a) & (b) & (c)\
end{tabular}
end{document}


The output is:
enter image description here



I set up the graph as a list of what a vertex is adjacent to; eg, H = Graph({1:[2], 2:[3], 3:[4], 4:[5], 5:1}) says that vertex 1 is adjacent to 2, vertex 2 is adjacent to 3, and so until vertex 5 is adjacent to 1. Setting a circular layout makes Sage place the vertices for you, and by setting options we can change the size of the graphic. So Sage creates the graph with sage{H} and the adjacency matrix with $sage{H.adjacency_matrix()}$.



By having a CAS do the work you can change the graph and SAGE will do the work without mistakes. This saves you having to code other examples and possibly making a mistake along the way.






share|improve this answer
























  • Not bad, not bad. Cocalc, huh? I use Overleaf (formerly ShareLaTeX). I'll check it out. Thanks.

    – tjt263
    5 hours ago













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2 Answers
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2 Answers
2






active

oldest

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active

oldest

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active

oldest

votes









6














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}


enter image description here






share|improve this answer


























  • Not bad, can we get the matrix lines drawn in or is it just like that

    – tjt263
    yesterday











  • @tjt263 Yes, sure.

    – marmot
    yesterday











  • Excellent. Wish I could go the other way. Maybe I will just try to draw them manually instead.

    – tjt263
    yesterday











  • What package can I draw them with manually? I like exactly how yours look.

    – tjt263
    23 hours ago













  • @tjt263 Sorry, I do not understand your question (because I do not know what "manually" means), nor your concerns. In order to draw these graphs, you need to know how they should look. The adjacency matrices have an almost minimal set of information. What kind of minimal set of information are you proposing to define the graphs?

    – marmot
    18 hours ago
















6














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}


enter image description here






share|improve this answer


























  • Not bad, can we get the matrix lines drawn in or is it just like that

    – tjt263
    yesterday











  • @tjt263 Yes, sure.

    – marmot
    yesterday











  • Excellent. Wish I could go the other way. Maybe I will just try to draw them manually instead.

    – tjt263
    yesterday











  • What package can I draw them with manually? I like exactly how yours look.

    – tjt263
    23 hours ago













  • @tjt263 Sorry, I do not understand your question (because I do not know what "manually" means), nor your concerns. In order to draw these graphs, you need to know how they should look. The adjacency matrices have an almost minimal set of information. What kind of minimal set of information are you proposing to define the graphs?

    – marmot
    18 hours ago














6












6








6







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}


enter image description here






share|improve this answer















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}


enter image description here







share|improve this answer














share|improve this answer



share|improve this answer








edited yesterday

























answered yesterday









marmotmarmot

112k5141266




112k5141266













  • Not bad, can we get the matrix lines drawn in or is it just like that

    – tjt263
    yesterday











  • @tjt263 Yes, sure.

    – marmot
    yesterday











  • Excellent. Wish I could go the other way. Maybe I will just try to draw them manually instead.

    – tjt263
    yesterday











  • What package can I draw them with manually? I like exactly how yours look.

    – tjt263
    23 hours ago













  • @tjt263 Sorry, I do not understand your question (because I do not know what "manually" means), nor your concerns. In order to draw these graphs, you need to know how they should look. The adjacency matrices have an almost minimal set of information. What kind of minimal set of information are you proposing to define the graphs?

    – marmot
    18 hours ago



















  • Not bad, can we get the matrix lines drawn in or is it just like that

    – tjt263
    yesterday











  • @tjt263 Yes, sure.

    – marmot
    yesterday











  • Excellent. Wish I could go the other way. Maybe I will just try to draw them manually instead.

    – tjt263
    yesterday











  • What package can I draw them with manually? I like exactly how yours look.

    – tjt263
    23 hours ago













  • @tjt263 Sorry, I do not understand your question (because I do not know what "manually" means), nor your concerns. In order to draw these graphs, you need to know how they should look. The adjacency matrices have an almost minimal set of information. What kind of minimal set of information are you proposing to define the graphs?

    – marmot
    18 hours ago

















Not bad, can we get the matrix lines drawn in or is it just like that

– tjt263
yesterday





Not bad, can we get the matrix lines drawn in or is it just like that

– tjt263
yesterday













@tjt263 Yes, sure.

– marmot
yesterday





@tjt263 Yes, sure.

– marmot
yesterday













Excellent. Wish I could go the other way. Maybe I will just try to draw them manually instead.

– tjt263
yesterday





Excellent. Wish I could go the other way. Maybe I will just try to draw them manually instead.

– tjt263
yesterday













What package can I draw them with manually? I like exactly how yours look.

– tjt263
23 hours ago







What package can I draw them with manually? I like exactly how yours look.

– tjt263
23 hours ago















@tjt263 Sorry, I do not understand your question (because I do not know what "manually" means), nor your concerns. In order to draw these graphs, you need to know how they should look. The adjacency matrices have an almost minimal set of information. What kind of minimal set of information are you proposing to define the graphs?

– marmot
18 hours ago





@tjt263 Sorry, I do not understand your question (because I do not know what "manually" means), nor your concerns. In order to draw these graphs, you need to know how they should look. The adjacency matrices have an almost minimal set of information. What kind of minimal set of information are you proposing to define the graphs?

– marmot
18 hours ago











2














Here is a sagetex solution which uses the computer algebra system, SAGE, to do the work. SAGE has built in knowledge of different classes of graphs and has some compatibility with LaTeX and Tikz and can solve some graph parameters as well. All that knowledge means SAGE is not part of the LaTeX distribution, but this is easily handled with a free Cocalc account. It might be my lack of knowledge about the subject but I had trouble trying to get the graphs to look exactly the way you have drawn them but if you're willing to give up some control here is a straightforward implementation of what you want.



documentclass{article}
usepackage{sagetex}
usepackage{tikz,tkz-graph,tkz-berge}
begin{document}
begin{sagesilent}
H = Graph({1:[2], 2:[3], 3:[4], 4:[5], 5:[1]})
H.set_pos(H.layout_circular()) #arrange the vertices in a circle
H.set_latex_options(scale=1.0,graphic_size=(3,3))
######
J = Graph({1:[2], 2:[5], 3:[4], 4:[1], 5:[3]})
J.set_pos(H.layout_circular()) #arrange the vertices in a circle
J.set_latex_options(scale=1.0,graphic_size=(3,3))
######
K = Graph({1:[3], 2:[4], 3:[5], 4:[1], 5:[2]})
K.set_pos(H.layout_circular()) #arrange the vertices in a circle
K.set_latex_options(scale=1.0,graphic_size=(3,3))
end{sagesilent}
Consider the three graphs below:\\

begin{tabular}{ccc}
begin{tikzpicture}
GraphInit[vstyle=Normal]
SetVertexNormal[Shape=circle,LineWidth = 1pt]
tikzset{EdgeStyle/.append style = {color = black, line width=1pt}}
sage{H}
end{tikzpicture} &
begin{tikzpicture}
GraphInit[vstyle=Normal]
SetVertexNormal[Shape=circle,LineWidth = 1pt]
tikzset{EdgeStyle/.append style = {color = black, line width=1pt}}
sage{J}
end{tikzpicture} &
begin{tikzpicture}
GraphInit[vstyle=Normal]
SetVertexNormal[Shape=circle,LineWidth = 1pt]
tikzset{EdgeStyle/.append style = {color = black, line width=1pt}}
sage{K}
end{tikzpicture}\
$sage{H.adjacency_matrix()}$ & $sage{J.adjacency_matrix()}$ & $sage{K.adjacency_matrix()}$\\
(a) & (b) & (c)\
end{tabular}
end{document}


The output is:
enter image description here



I set up the graph as a list of what a vertex is adjacent to; eg, H = Graph({1:[2], 2:[3], 3:[4], 4:[5], 5:1}) says that vertex 1 is adjacent to 2, vertex 2 is adjacent to 3, and so until vertex 5 is adjacent to 1. Setting a circular layout makes Sage place the vertices for you, and by setting options we can change the size of the graphic. So Sage creates the graph with sage{H} and the adjacency matrix with $sage{H.adjacency_matrix()}$.



By having a CAS do the work you can change the graph and SAGE will do the work without mistakes. This saves you having to code other examples and possibly making a mistake along the way.






share|improve this answer
























  • Not bad, not bad. Cocalc, huh? I use Overleaf (formerly ShareLaTeX). I'll check it out. Thanks.

    – tjt263
    5 hours ago


















2














Here is a sagetex solution which uses the computer algebra system, SAGE, to do the work. SAGE has built in knowledge of different classes of graphs and has some compatibility with LaTeX and Tikz and can solve some graph parameters as well. All that knowledge means SAGE is not part of the LaTeX distribution, but this is easily handled with a free Cocalc account. It might be my lack of knowledge about the subject but I had trouble trying to get the graphs to look exactly the way you have drawn them but if you're willing to give up some control here is a straightforward implementation of what you want.



documentclass{article}
usepackage{sagetex}
usepackage{tikz,tkz-graph,tkz-berge}
begin{document}
begin{sagesilent}
H = Graph({1:[2], 2:[3], 3:[4], 4:[5], 5:[1]})
H.set_pos(H.layout_circular()) #arrange the vertices in a circle
H.set_latex_options(scale=1.0,graphic_size=(3,3))
######
J = Graph({1:[2], 2:[5], 3:[4], 4:[1], 5:[3]})
J.set_pos(H.layout_circular()) #arrange the vertices in a circle
J.set_latex_options(scale=1.0,graphic_size=(3,3))
######
K = Graph({1:[3], 2:[4], 3:[5], 4:[1], 5:[2]})
K.set_pos(H.layout_circular()) #arrange the vertices in a circle
K.set_latex_options(scale=1.0,graphic_size=(3,3))
end{sagesilent}
Consider the three graphs below:\\

begin{tabular}{ccc}
begin{tikzpicture}
GraphInit[vstyle=Normal]
SetVertexNormal[Shape=circle,LineWidth = 1pt]
tikzset{EdgeStyle/.append style = {color = black, line width=1pt}}
sage{H}
end{tikzpicture} &
begin{tikzpicture}
GraphInit[vstyle=Normal]
SetVertexNormal[Shape=circle,LineWidth = 1pt]
tikzset{EdgeStyle/.append style = {color = black, line width=1pt}}
sage{J}
end{tikzpicture} &
begin{tikzpicture}
GraphInit[vstyle=Normal]
SetVertexNormal[Shape=circle,LineWidth = 1pt]
tikzset{EdgeStyle/.append style = {color = black, line width=1pt}}
sage{K}
end{tikzpicture}\
$sage{H.adjacency_matrix()}$ & $sage{J.adjacency_matrix()}$ & $sage{K.adjacency_matrix()}$\\
(a) & (b) & (c)\
end{tabular}
end{document}


The output is:
enter image description here



I set up the graph as a list of what a vertex is adjacent to; eg, H = Graph({1:[2], 2:[3], 3:[4], 4:[5], 5:1}) says that vertex 1 is adjacent to 2, vertex 2 is adjacent to 3, and so until vertex 5 is adjacent to 1. Setting a circular layout makes Sage place the vertices for you, and by setting options we can change the size of the graphic. So Sage creates the graph with sage{H} and the adjacency matrix with $sage{H.adjacency_matrix()}$.



By having a CAS do the work you can change the graph and SAGE will do the work without mistakes. This saves you having to code other examples and possibly making a mistake along the way.






share|improve this answer
























  • Not bad, not bad. Cocalc, huh? I use Overleaf (formerly ShareLaTeX). I'll check it out. Thanks.

    – tjt263
    5 hours ago
















2












2








2







Here is a sagetex solution which uses the computer algebra system, SAGE, to do the work. SAGE has built in knowledge of different classes of graphs and has some compatibility with LaTeX and Tikz and can solve some graph parameters as well. All that knowledge means SAGE is not part of the LaTeX distribution, but this is easily handled with a free Cocalc account. It might be my lack of knowledge about the subject but I had trouble trying to get the graphs to look exactly the way you have drawn them but if you're willing to give up some control here is a straightforward implementation of what you want.



documentclass{article}
usepackage{sagetex}
usepackage{tikz,tkz-graph,tkz-berge}
begin{document}
begin{sagesilent}
H = Graph({1:[2], 2:[3], 3:[4], 4:[5], 5:[1]})
H.set_pos(H.layout_circular()) #arrange the vertices in a circle
H.set_latex_options(scale=1.0,graphic_size=(3,3))
######
J = Graph({1:[2], 2:[5], 3:[4], 4:[1], 5:[3]})
J.set_pos(H.layout_circular()) #arrange the vertices in a circle
J.set_latex_options(scale=1.0,graphic_size=(3,3))
######
K = Graph({1:[3], 2:[4], 3:[5], 4:[1], 5:[2]})
K.set_pos(H.layout_circular()) #arrange the vertices in a circle
K.set_latex_options(scale=1.0,graphic_size=(3,3))
end{sagesilent}
Consider the three graphs below:\\

begin{tabular}{ccc}
begin{tikzpicture}
GraphInit[vstyle=Normal]
SetVertexNormal[Shape=circle,LineWidth = 1pt]
tikzset{EdgeStyle/.append style = {color = black, line width=1pt}}
sage{H}
end{tikzpicture} &
begin{tikzpicture}
GraphInit[vstyle=Normal]
SetVertexNormal[Shape=circle,LineWidth = 1pt]
tikzset{EdgeStyle/.append style = {color = black, line width=1pt}}
sage{J}
end{tikzpicture} &
begin{tikzpicture}
GraphInit[vstyle=Normal]
SetVertexNormal[Shape=circle,LineWidth = 1pt]
tikzset{EdgeStyle/.append style = {color = black, line width=1pt}}
sage{K}
end{tikzpicture}\
$sage{H.adjacency_matrix()}$ & $sage{J.adjacency_matrix()}$ & $sage{K.adjacency_matrix()}$\\
(a) & (b) & (c)\
end{tabular}
end{document}


The output is:
enter image description here



I set up the graph as a list of what a vertex is adjacent to; eg, H = Graph({1:[2], 2:[3], 3:[4], 4:[5], 5:1}) says that vertex 1 is adjacent to 2, vertex 2 is adjacent to 3, and so until vertex 5 is adjacent to 1. Setting a circular layout makes Sage place the vertices for you, and by setting options we can change the size of the graphic. So Sage creates the graph with sage{H} and the adjacency matrix with $sage{H.adjacency_matrix()}$.



By having a CAS do the work you can change the graph and SAGE will do the work without mistakes. This saves you having to code other examples and possibly making a mistake along the way.






share|improve this answer













Here is a sagetex solution which uses the computer algebra system, SAGE, to do the work. SAGE has built in knowledge of different classes of graphs and has some compatibility with LaTeX and Tikz and can solve some graph parameters as well. All that knowledge means SAGE is not part of the LaTeX distribution, but this is easily handled with a free Cocalc account. It might be my lack of knowledge about the subject but I had trouble trying to get the graphs to look exactly the way you have drawn them but if you're willing to give up some control here is a straightforward implementation of what you want.



documentclass{article}
usepackage{sagetex}
usepackage{tikz,tkz-graph,tkz-berge}
begin{document}
begin{sagesilent}
H = Graph({1:[2], 2:[3], 3:[4], 4:[5], 5:[1]})
H.set_pos(H.layout_circular()) #arrange the vertices in a circle
H.set_latex_options(scale=1.0,graphic_size=(3,3))
######
J = Graph({1:[2], 2:[5], 3:[4], 4:[1], 5:[3]})
J.set_pos(H.layout_circular()) #arrange the vertices in a circle
J.set_latex_options(scale=1.0,graphic_size=(3,3))
######
K = Graph({1:[3], 2:[4], 3:[5], 4:[1], 5:[2]})
K.set_pos(H.layout_circular()) #arrange the vertices in a circle
K.set_latex_options(scale=1.0,graphic_size=(3,3))
end{sagesilent}
Consider the three graphs below:\\

begin{tabular}{ccc}
begin{tikzpicture}
GraphInit[vstyle=Normal]
SetVertexNormal[Shape=circle,LineWidth = 1pt]
tikzset{EdgeStyle/.append style = {color = black, line width=1pt}}
sage{H}
end{tikzpicture} &
begin{tikzpicture}
GraphInit[vstyle=Normal]
SetVertexNormal[Shape=circle,LineWidth = 1pt]
tikzset{EdgeStyle/.append style = {color = black, line width=1pt}}
sage{J}
end{tikzpicture} &
begin{tikzpicture}
GraphInit[vstyle=Normal]
SetVertexNormal[Shape=circle,LineWidth = 1pt]
tikzset{EdgeStyle/.append style = {color = black, line width=1pt}}
sage{K}
end{tikzpicture}\
$sage{H.adjacency_matrix()}$ & $sage{J.adjacency_matrix()}$ & $sage{K.adjacency_matrix()}$\\
(a) & (b) & (c)\
end{tabular}
end{document}


The output is:
enter image description here



I set up the graph as a list of what a vertex is adjacent to; eg, H = Graph({1:[2], 2:[3], 3:[4], 4:[5], 5:1}) says that vertex 1 is adjacent to 2, vertex 2 is adjacent to 3, and so until vertex 5 is adjacent to 1. Setting a circular layout makes Sage place the vertices for you, and by setting options we can change the size of the graphic. So Sage creates the graph with sage{H} and the adjacency matrix with $sage{H.adjacency_matrix()}$.



By having a CAS do the work you can change the graph and SAGE will do the work without mistakes. This saves you having to code other examples and possibly making a mistake along the way.







share|improve this answer












share|improve this answer



share|improve this answer










answered 15 hours ago









DJPDJP

7,91921732




7,91921732













  • Not bad, not bad. Cocalc, huh? I use Overleaf (formerly ShareLaTeX). I'll check it out. Thanks.

    – tjt263
    5 hours ago





















  • Not bad, not bad. Cocalc, huh? I use Overleaf (formerly ShareLaTeX). I'll check it out. Thanks.

    – tjt263
    5 hours ago



















Not bad, not bad. Cocalc, huh? I use Overleaf (formerly ShareLaTeX). I'll check it out. Thanks.

– tjt263
5 hours ago







Not bad, not bad. Cocalc, huh? I use Overleaf (formerly ShareLaTeX). I'll check it out. Thanks.

– tjt263
5 hours ago




















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