The core operation in a GNN is message passing: each node collects information from its neighbors, aggregates it (sum, mean, or attention-weighted), and updates its own representation. After K rounds of message passing, each node's representation encodes information about its K-hop neighborhood. Graph Convolutional Networks (GCN), GraphSAGE, and Graph Attention Networks (GAT) are the most common architectures, differing in how they aggregate neighbor information.
Drug discovery: molecules are graphs (atoms = nodes, bonds = edges). GNNs predict molecular properties, binding affinity, and toxicity by learning from the molecular graph structure. Social networks: GNNs detect communities, predict links, and identify influential nodes. Recommendation systems: users and items form a bipartite graph, and GNNs predict which items a user would like based on graph structure. Fraud detection: transaction networks reveal suspicious patterns that GNNs can learn to identify.
There's a deep connection between Transformers and GNNs: self-attention can be viewed as message passing on a fully connected graph (every token attends to every other token). GNNs operate on sparse graphs (each node only connects to its actual neighbors). This connection has inspired Graph Transformers that combine the expressiveness of Transformers with the efficiency of sparse graph structures, and has led to cross-pollination of ideas between the two communities.