Cycle . graph theory

Set

 context $V,E$ … set
 definiendum $\langle V,E,\psi\rangle \in \mathrm{it}(E,V)$
 inclusion $\langle V,E,\psi\rangle$ … path postulate $|V|\ge 3$
 range $u,v\in V$ range $a$ … sequence in $V,\ \forall i.\ a_{i+|V|}=a_i$ range $i\in\mathbb N$
 postulate $\exists a.\ \forall u,v.\ (\exists i.\ \{a_{i},a_{i+1}\}=\{u,v\}) \leftrightarrow (\{u,v\}\dots\mathrm{edge})$

Discussion

A path is a graph which can fully be described by a repeating sequence of vertices.