normal directed graph = line graph

"we the meaning"

base for complements is undefined:
Paths[G](main,t) where t in Reach[G](main)

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via(p1,p2) p1 => S1, p2 => S2
union Paths[G](main,s) . Paths[G](s,t), where s in S1 and t in S2
(s,t)