A transit function $R$ on a set $V$ is a function $R\:V\times V\rightarrow 2^{V}$ satisfying the axioms $u\in R(u,v)$, $R(u,v)=R(v,u)$ and $R(u,u)=\lbrace u\rbrace $, for all $u,v \in V$. The all-paths transit function of a connected graph is characterized by transit axioms.