Btukfyl

I'm trying to use layered graph layouts to generate Directed Acyclic Graphs where all nodes are partitioned into layers. The following code produces a near-perfect result.

RequirePackage{luatex85}

documentclass{article}



usepackage{graphicx}

usepackage{subcaption}

usepackage{a4wide}



usepackage{tikz}

usetikzlibrary{graphs,graphdrawing,quotes}

usegdlibrary{layered}



begin{document}

begin{figure}

centering

begin{subfigure}{0.3textwidth}

centering

begin{tikzpicture}[rounded corners]

graph [layered layout,

edge quotes={fill=white,inner sep=1pt,font=scriptsize},

nodes={circle,draw,inner sep=.2,outer sep=0, minimum size=.45cm},

level sep=1.5cm, %vertical distance between layers

sibling distance=2cm, %distance between nodes of the same connected component in the same layer

component sep=0cm %distance between connected components

]

{

{

[nodes={draw=none,text opacity=0}, edge={draw=none}]

l0 ->["$v0$"] l1 ->["$v1$"] l2 ->["$v2$"] l3 ->["$v4$"] l4 ->["$v5$"] l5;

},

{[edge={pos=.45}]

r/"$r$";

t/"$t$";

2/"$u_{2}$";

3/"$u_{3}$";

4/"$u_{4}$";

5/"$u_{5}$";

6/"$u_{6}$";

7/"$u_{7}$";

8/"$u_{8}$";

9/"$u_{9}$";

10/"$u_{10}$";

11/"$u_{11}$";

12/"$u_{12}$";

r ->["$0$",bend left=0] 2,

r ->["$1$",bend left=0] 3,

2 ->["$0$",bend left=0] 4,

2 ->["$1$",bend left=0] 5,

3 ->["$0$",bend left=0] 6,

3 ->["$1$",bend left=0] 4,

4 ->["$0$",bend left=0] 7,

4 ->["$1$",bend left=0] 8,

5 ->["$0$",bend left=0] 9,

5 ->["$1$",bend left=0] 7,

6 ->["$0$",bend left=0] 8,

6 ->["$1$",bend left=0] 9,

7 ->["$0$",bend left=0] 10,

7 ->["$1$",bend left=0] 11,

8 ->["$0$",bend left=0] 12,

8 ->["$1$",bend left=0] 10,

9 ->["$0$",bend left=0] 11,

9 ->["$1$",bend left=0] 12,

10 ->["$1$",bend left=-80] t,

10 ->["$4$",bend left=-60] t,

10 ->["$7$",bend left=-40] t,

10 ->["$10$",bend left=-20] t,

10 ->["$13$",bend left=0] t,

10 ->["$16$",bend left=20] t,

10 ->["$19$",bend left=40] t,

10 ->["$22$",bend left=60] t,

10 ->["$25$",bend left=80] t,

11 ->["$0$",bend left=-80] t,

11 ->["$3$",bend left=-60] t,

11 ->["$6$",bend left=-40] t,

11 ->["$9$",bend left=-20] t,

11 ->["$12$",bend left=0] t,

11 ->["$15$",bend left=20] t,

11 ->["$18$",bend left=40] t,

11 ->["$21$",bend left=60] t,

11 ->["$24$",bend left=80] t,

12 ->["$2$",bend left=-80] t,

12 ->["$5$",bend left=-60] t,

12 ->["$8$",bend left=-40] t,

12 ->["$11$",bend left=-20] t,

12 ->["$14$",bend left=0] t,

12 ->["$17$",bend left=20] t,

12 ->["$20$",bend left=40] t,

12 ->["$23$",bend left=60] t,

}

};

begin{scope}[node distance=.4cm,font=scriptsize]

node[right of=r]{$0$};

node[right of=t]{$1$};

node[right of=2]{$0$};

node[right of=3]{$2$};

node[right of=4]{$0$};

node[right of=5]{$1$};

node[right of=6]{$2$};

node[right of=7]{$0$};

node[right of=8]{$2$};

node[right of=9]{$1$};

node[right of=10]{$0$};

node[right of=11]{$1$};

node[right of=12]{$2$};

end{scope}

end{tikzpicture}

caption{c0(mod5)}

end{subfigure}

caption{test 0}

end{figure}

end{document}

Notice that for some weird reason, vertex t is placed in the same layer as u7, u8, u9, resulting in a lot of edge overlap. Vertex t should have been placed in a new layer, below the layer containing vertices u10, u11, u12. Is there a way I can force this?

According to the Tikz manual chapter 31st, the layered layout algorithm performs the following steps:

1. Cycle removal.


2. Layer assignment (sometimes called node ranking).


3. Crossing minimization (also referred to as node ordering).


4. Node positioning (or coordinate assignment).


5. Edge routing.

Technically I don't need steps 1,2,5 because I already know the layers for each node, and my graph is guaranteed not to contain cycles. I do however need step 3 to determine the ordering of nodes in each layer to minimize crossings, as well as step 4 to determine coordinates.