Then $\Gamma$ is $c$-cyclically monotone, in the sense that for every $N \in \mathbb{N}$ and every finite family $(x_i,y_i)_{i=1}^N \subset \Gamma$ with indices taken cyclically by setting $y_{N+1}:=y_1$,
if and only if $\Gamma$, viewed as a subset of $\mathbb{R}^d \times \mathbb{R}^d$ with second coordinate denoted by $p$, is cyclically monotone in the classical sense, namely for every $N \in \mathbb{N}$ and every finite family $(x_i,p_i)_{i=1}^N \subset \Gamma$ with $x_{N+1}:=x_1$,