Algorithm 1: GN block without global variables [6].

functionGraphNetwork (E, V)     for $k\in \{1\dots N^e\}$ do         ${\mathbf{e}}_k^{\prime }\leftarrow {\varphi }^e\left({\mathbf{e}}_k,{\mathbf{v}}_{r_k},{\mathbf{v}}_{s_k}\right)$                         ▹ 1. Compute updated edges     end for     for $i\in \{1\dots N^n\}$ do         let $E_i^{\prime }={\left\{\left({\mathbf{e}}_k^{\prime },r_k,s_k\right)\right\}}_{r_k=i,k=1:N^e}$         ${\overline{\mathbf{e}}}_i^{\prime }\leftarrow {\rho }^{e\to v}\left(E_i^{\prime }\right)$                                    ▹ 2. Aggregate edges per node         ${\mathbf{v}}_i^{\prime }\leftarrow {\varphi }^v\left({\overline{\mathbf{e}}}_i^{\prime },{\mathbf{v}}_i,\right)$                                    ▹ 3. Compute updated nodes     end for     let $V^{\prime }={\left\{{\mathbf{v}}^{\prime }\right\}}_{i=1:N^v}$     let $E^{\prime }={\left\{\left({\mathbf{e}}_k^{\prime },r_k,s_k\right)\right\}}_{k=1:N^e}$     return $(E^{\prime },V^{\prime })$ end function