During each message-passing iteration in a Graph Neural Network (GNN), a hidden embedding $h^{(k)}_u$ corresponding to each node $u \in V$ is updated according to information aggregated from $u$’s graph neighborhood $N(u)$. The message-passing update can be expressed by: h^{(k+1)}_u = UPDATE^{(k)}(h^{(k)}_u, AGGREGATE^{(k)}({h^{(k)}_v, forall v in N(u)})) or alternatively as: h^{(k+1)}_u = UPDATE^{(k)}(h^{(k)}u, m^{(k)}{N(u)}) where $UPDATE$ and $AGGREGATE$ are arbitrary differentiable functions (neural networks) and $m_{N(u)}$ is the "message" that is aggregated from $u$'s graph neighborhood $N(u)$.