Simple graph

Set

 context $V,E$ … set
 definiendum $\langle V,E,\psi\rangle \in \mathrm{it}(E,V)$
 postulate $\langle V,E,\psi\rangle$ … loopless graph
 postulate $\psi$ … injective

Discussion

Two vertices $\{u,v\}$ of a a simple graph are connected by at most one edge.