The All-Paths Transit Function of a Graph
Manoj Changat, Sandi Klavžar, Henry Martyn Mulder · Czechoslovak Mathematical Journal · 2001
A transit function R on a set V is a function $$R:VxV \to 2^2 $$ satisfying the axioms $$u \in R(u,\upsilon ),R(u,\upsilon ) = R(\upsilon ,u)$$ and $$R(u,u) = \{ u\} $$ , for all $$u,\upsilon \in V$$ . The all-paths transit function of a connected graph is characterized by transit axioms.