the creation of a graph with some specific attributes is for me not possible. Maybe you have some helpfully ideas how to realize?!
The attributes of the graphs in 1. and 2. have to be "mixed", while in 3. the style of the link connection between parent and outgoing chain (child) is a nice to have option.
1. To save space the "layered layout" is preferred but without the labyrinthine chain structure, see lower figure (B). For example, instead of the structure
1-3 -> 5-1 (same line)
-> 1-4 (new line)
it has to look like
1-3 -> 1-4 (same line)
-> 5-1 (new line)
2. From the parent chain several child chains can be branched. All chain links from the parent chain have to be in the same line, like in the upper figure (A).
3. The initial link of each outgoing chain (child with the attributes [>red, bend right, very thick]) must be a rectangle instead of a straight line.
Thank you for your help!
\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{graphs}
\usetikzlibrary{graphdrawing}
\usegdlibrary{layered}
\begin{document}
\tikz [
rotate=90,
]
\graph [
]{
"1-1" -> {
"1-2" -> "1-3" ->{
"1-4" ->"1-5"->{
"1-6",
"2-1"[>red, bend right, very thick]
->"2-2"->{
"2-3",
"4-1"[>red, bend right, very thick]
},
},
"5-1"[>red, bend right, very thick]
->"5-2"->"5-3"->"5-4"
},
"3-1"[>red, bend right, very thick]
->"3-2"->"3-3"->"3-4"->"3-5"->"3-6"->"3-7"->"3-8"->"3-9"->"3-10"->"3-11"->"3-12"
}
};
\hspace{2cm}
\tikz [
layered layout,
rotate=90
]
\graph [
]{
"1-1" -> {
"1-2" -> "1-3" ->{
"1-4" ->"1-5"->{
"1-6",
"2-1"[>red, bend right, very thick]
->"2-2"->{
"2-3",
"4-1"[>red, bend right, very thick]
},
},
"5-1"[>red, bend right, very thick]
->"5-2"->"5-3"->"5-4"
},
"3-1"[>red, bend right, very thick]
->"3-2"->"3-3"->"3-4"->"3-5"->"3-6"->"3-7"->"3-8"->"3-9"->"3-10"->"3-11"->"3-12"
}
};
\end{document}


