I want to draw the graph (ladder track representation) as follows:

i.e. without node shapes and with two edge labels: at head and at tail of edge.
What should I do to achieve this?
(14, 15 — nodes with two edges each)
I want to draw the graph (ladder track representation) as follows: i.e. without node
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Almost ugly solution (do edit if you can improve correctness):
which leads to