In your comment you mentioned using the graphics in a research article. That means working with Sage alone isn't good enough because journals are notoriously picky. Many don't want color and are specific about the font and fontsize you're using. LaTeX is the best tool. You can use Sage along with the sagetex package and tkz-graph and tkz-berge to do a lot of the difficult work for you. See Alain Matthes answer here for more on typesetting graphs. Here is some sample code using the preamble code mentioned in your comment above.
\documentclass[border={2mm 2mm 8mm 8mm}]{standalone}
\usepackage{sagetex,xcolor,tikz,tkz-graph,tkz-berge,tikz-cd}
\usetikzlibrary{matrix,patterns,shapes,decorations.pathmorphing,decorations.pathreplacing,calc,arrows}
\begin{document}
\begin{sagesilent}
def from_QPA(Q):
arrows = [(v.SourceOfPath(), v.TargetOfPath(), v) for v in Q.ArrowsOfQuiver() ]
elements = Q.VerticesOfQuiver()
return DiGraph([elements, arrows],loops=True,format='vertices_and_edges')
libgap.LoadPackage("QPA")
Q = libgap.Quiver( ["v1","v2","v3","v4","v5","v6","v7","v8","v9","v10","v11","v12","v13","v14","v15"], [["v1","v3","a1"],["v2","v1","a2"],["v3","v8","a3"],["v4","v6","a4"],["v5","v6","a5"]
,["v6","v4","a6"],["v6","v5","a7"],["v6","v8","a8"],["v7","v12","a9"],["v8","v9","a10"],["v8","v10","a11"],["v9","v7","a12"],["v9","v11","a13"],["v10","v7","a14"],["v10","v11","
a15"],["v11","v12","a16"],["v12","v2","a17"],["v12","v13","a18"],["v13","v14","a19"], ["v13","v15","a20"],["v14","v13","a21"],["v15","v13","a22"]] )
U=from_QPA(Q)
U.set_latex_options(graphic_size=(20,20), vertex_labels=True,edge_labels=True)
Ustring = latex(U)
\end{sagesilent}
\sagestr{Ustring}
\end{document}
The result running in Cocalc is:
Notice that the picture shows that LaTeX is complaining of an error but a picture renders. You said you aren't getting errors; maybe a more current versions? Each time you Build the code you'll get a different drawing of the graph so you will want to capture the look in order for you to handle the almost certain revisions they will want you to make. When you find a picture which is close to your satisfaction, take the code from your .sout file:
Now you can copy this code (I have copied and modified code from a different Build) to get something like this:
\documentclass[11pt,border={10pt 10pt 10pt 10pt}]{standalone}
\usepackage{sagetex,xcolor,tikz,tkz-graph,tkz-berge,tikz-cd}
\usetikzlibrary{matrix,patterns,shapes,decorations.pathmorphing,decorations.pathreplacing,calc,arrows}
\begin{document}
\begin{sagesilent}
a = 3.75
b = 3.75
output = r"\begin{tikzpicture}"
output += r"\Vertex[style={minimum size=1.0cm,shape=circle},LabelOut=false,L=\hbox{$v_0$},x=%s cm,y=%s cm]{v0}"%(3.2737*a,0.5293*b)
output += r"\Vertex[style={minimum size=1.0cm,shape=circle},LabelOut=false,L=\hbox{$v_1$},x=%s cm,y= %s cm]{v1}"%(3.5269*a,1.7219*b)
output += r"\Vertex[style={minimum size=1.0cm,shape=circle},LabelOut=false,L=\hbox{$v_2$},x= %s cm,y=%s cm]{v2}"%(2.4491*a,0.527*b)
output += r"\Vertex[style={minimum size=1.0cm,shape=circle},LabelOut=false,L=\hbox{$v_3$},x=%s cm,y=%s cm]{v3}"%(0.0*a,0.9498*b)
output += r"\Vertex[style={minimum size=1.0cm,shape=circle},LabelOut=false,L=\hbox{$v_4$},x=%s cm,y=%s cm]{v4}"%(0.4106*a,0.0*b)
output += r"\Vertex[style={minimum size=1.0cm,shape=circle},LabelOut=false,L=\hbox{$v_5$},x=%s cm,y=%s cm]{v5}"%(0.8179*a,0.8914*b)
output += r"\Vertex[style={minimum size=1.0cm,shape=circle},LabelOut=false,L=\hbox{$v_6$},x=%s cm,y=%s cm]{v6}"%(2.3603*a,3.4245*b)
output += r"\Vertex[style={minimum size=1.0cm,shape=circle},LabelOut=false,L=\hbox{$v_7$},x=%s cm,y=%s cm]{v7}"%(1.7828*a,1.4959*b)
output += r"\Vertex[style={minimum size=1.0cm,shape=circle},LabelOut=false,L=\hbox{$v_8$},x=%s cm,y=%s cm]{v8}"%(1.7707*a,2.778*b)
output += r"\Vertex[style={minimum size=1.0cm,shape=circle},LabelOut=false,L=\hbox{$v_9$},x=%s cm,y=%s cm]{v9}"%(2.1004*a,2.4636*b)
output += r"\Vertex[style={minimum size=1.0cm,shape=circle},LabelOut=false,L=\hbox{$v_{10}$},x=%s cm,y=%s cm]{v10}"%(2.5107*a,2.9341*b)
output += r"\Vertex[style={minimum size=1.0cm,shape=circle},LabelOut=false,L=\hbox{$v_{11}$},x=%s cm,y=%s cm]{v11}"%(3.2906*a,3.092*b)
output += r"\Vertex[style={minimum size=1.0cm,shape=circle},LabelOut=false,L=\hbox{$v_{12}$},x=%s cm,y=%s cm]{v12}"%(4.2021*a,4.0255*b)
output += r"\Vertex[style={minimum size=1.0cm,shape=circle},LabelOut=false,L=\hbox{$v_{13}$},x=%s cm,y=%s cm]{v13}"%(4.485*a,5.0*b)
output += r"\Vertex[style={minimum size=1.0cm,shape=circle},LabelOut=false,L=\hbox{$v_{14}$},x=%s cm,y=%s cm]{v14}"%(5.0*a,4.1315*b)
output += r"\Edge[lw=0.1cm,style={post, bend right,},](v0)(v2)"
output += r"\Edge[lw=0.1cm,style={post, bend right,},](v1)(v0)"
output += r"\Edge[lw=0.1cm,style={post, bend right,},](v2)(v7)"
output += r"\Edge[lw=0.1cm,style={post, bend right,},](v3)(v5)"
output += r"\Edge[lw=0.1cm,style={post, bend right,},](v4)(v5)"
output += r"\Edge[lw=0.1cm,style={post, bend right,},](v5)(v3)"
output += r"\Edge[lw=0.1cm,style={post, bend right,},](v5)(v4)"
output += r"\Edge[lw=0.1cm,style={post, straight,},label=$a_8$](v5)(v7)"
output += r"\Edge[lw=0.1cm,style={post, bend right,},](v6)(v11)"
output += r"\Edge[lw=0.1cm,style={post, bend right,},](v7)(v8)"
output += r"\Edge[lw=0.1cm,style={post, bend right,},](v7)(v9)"
output += r"\Edge[lw=0.1cm,style={post, straight,},](v8)(v6)"
output += r"\Edge[lw=0.1cm,style={post, bend right,},](v8)(v10)"
output += r"\Edge[lw=0.1cm,style={post, straight,},](v9)(v6)"
output += r"\Edge[lw=0.1cm,style={post, bend right,},](v9)(v10)"
output += r"\Edge[lw=0.1cm,style={post, bend right,},](v10)(v11)"
output += r"\Edge[lw=0.1cm,style={post, bend right},](v11)(v1)"
output += r"\Edge[lw=0.1cm,style={post, straight,},label=$a_{18}$](v11)(v12)"
output += r"\Edge[lw=0.1cm,style={post, bend right,},](v12)(v13)"
output += r"\Edge[lw=0.1cm,style={post, bend right,},](v12)(v14)"
output += r"\Edge[lw=0.1cm,style={post, bend right,},](v13)(v12)"
output += r"\Edge[lw=0.1cm,style={post, bend right,},](v14)(v12)"
output += r"\end{tikzpicture}"
\end{sagesilent}
\sagestr{output}
\end{document}
Placing the code of each line in raw strings; e.g., output = r"\begin{tikzpicture}" is going to allow you to fine tune the positioning with the help of the coordinates you liked and picking your own values of a and b. I've taken the positions from a picture that looked satisfactory to me and by adjusting, such as in 3.2737*a,0.5293*b I can stretch the graph to make the graph even better. You can modify vertices, remove labels and make your directed edges straight, if you want. For example, output += r"\Edge[lw=0.1cm,style={post, straight,},label=$a_{18}$](v11)(v12)" creates a straight directed edge with a label.
The answer to Question 1 is then: Use the packages tkz-berge, tkz-graph, and sagetex to create your picture. Sage will do the calculations but LaTeX will handle the picture. With respect to Question 2, I don't think there is a better way than what I'm suggesting because Sage is doing the calculations using the GAP-package QPA.
figsizeto make it look better; egdisplay(U.plot(edge_labels=True,figsize=[25,25])). Now the graph doesn't look terrible to me. – DJP Jan 10 '21 at 15:14L=\hbox{$\text{\texttt{v1}}$}might be a result of creating a Digraph after QPA. Can you post your LaTeX code that runs the code snippet fromlatex(U)? – DJP Jan 10 '21 at 19:07Undefined control sequence. \cmdGR@vertex@L ->\hbox {$\text {\texttt {v1}}$}. This will make it difficult for me to check. – DJP Jan 10 '21 at 21:12