The Math Behind GNN The core of a Graph Neural Network (GNN) lies in its message-passing mechanism, which allows nodes to iteratively update their representations by aggregating information from their neighbors. A general formula for the update rule of a node $v$ at layer $l+1$ can be expressed as: $$ h_v^{(l+1)} = \sigma \left( W^{(l)} \sum_{u \in \mathcal{N}(v) \cup v} \frac{h_u^{(l)}}{| \mathcal{N}(v)|} \right) $$ Let’s break down this formula: $h_v^{(l+1)}$: This is the new feature vector (or embedding) of our target node $v$ at the next layer, $l+1$. This is what we want to compute. ...