Graph Neural Networks (GNNs) are neural models that operate on graphs G = (V, E), where V represents the set of nodes and E the set of edges.
The central operation in GNNs is iterative message passing, where for each node v ∈ V an improved node representation vector h_v^{(k)} in the k-th layer is computed by aggregating the representations of its neighbors:
h_v^{(k)} = σ \left( W^{(k)} \cdot \text{AGGREGATE} \left( \{ h_u^{(k-1)} : u \in \mathcal{N}(v) \} \right) + b^{(k)} \right)
Here, σ is an activation function, W^{(k)} and b^{(k)} are learnable parameters, and \mathcal{N}(v) is the neighborhood of v.
The aggregation function can take various forms, such as mean, sum, or weighted combinations, as in Graph Attention Networks (Velickovic et al., 2018).
GNNs enable the modeling of complex relational structures and are successfully applied in many domains, including chemoinformatics, social networks, and knowledge graphs.
Definition:
Graph Neural Networks are neural networks that learn by iterative aggregation and transformation of neighborhood information in graphs to produce node, edge, or graph representations.
Source:
Wu, Z., Pan, S., Chen, F., Long, G., Zhang, C., & Philip, S. Y. (2021). A Comprehensive Survey on Graph Neural Networks. IEEE Transactions on Neural Networks and Learning Systems.