Graph Neural Network (GNN)

The fundamental computational mechanism of GNNs where nodes iteratively exchange information with their neighbors. In each layer, a node aggregates feature vectors from its local neighborhood, applies a learnable transformation function, and updates its own hidden state. This process captures both local structural patterns and node feature distributions. After k message-passing iterations, a node's representation encodes information from its k-hop neighborhood, enabling the model to learn hierarchical graph representations without requiring a fixed input size.

A seminal GNN variant that generalizes the convolution operation to irregular graph domains. GCNs use a spectral or spatial approach to aggregate neighbor features with a normalized adjacency matrix. The layer-wise propagation rule applies a first-order approximation of spectral graph convolutions, making it computationally efficient. Key characteristics include:

• Transductive learning: requires the full graph structure during training
• Weight sharing: same transformation applied across all nodes
• Semi-supervised node classification: excels when labels are scarce but graph structure is rich

A GNN architecture that introduces attention mechanisms to weigh the importance of neighboring nodes during aggregation. Instead of treating all neighbors equally, GATs compute dynamic attention coefficients using a shared self-attention mechanism. This allows the model to:

• Focus on relevant neighbors and ignore noisy connections
• Handle heterogeneous degree distributions without sampling
• Achieve inductive capability by learning attention functions rather than relying on global graph structure Multi-head attention further stabilizes the learning process by computing multiple parallel attention distributions.

An inductive framework that generates node embeddings by sampling and aggregating features from a node's local neighborhood. Unlike transductive methods, GraphSAGE learns aggregator functions (mean, LSTM, pooling) that generalize to unseen nodes and entirely new graphs. The sampling strategy controls the computational footprint by limiting the neighborhood size. This architecture is foundational for large-scale industrial applications where graphs evolve continuously and full-batch training is infeasible, such as dynamic social networks and recommendation systems.

The process of mapping graph nodes to low-dimensional continuous vector spaces that preserve structural and relational properties. Embeddings encode topological similarity—nodes with similar neighborhoods receive similar vectors—and feature similarity from node attributes. These dense representations serve as feature inputs for downstream tasks like classification, clustering, and link prediction. Classical methods like DeepWalk and node2vec use random walks to capture graph structure, while GNN-based embeddings incorporate both structure and node features through end-to-end differentiable learning.

A core graph learning task that predicts the existence or likelihood of missing edges between node pairs. GNNs approach this by computing pairwise node similarity scores from learned embeddings using decoders like dot product or DistMult. Applications include:

• Knowledge graph completion: predicting missing facts in triple stores
• Recommender systems: suggesting new user-item interactions
• Drug discovery: predicting protein-protein or drug-target interactions
• Social network analysis: forecasting future connections The task evaluates a model's ability to capture relational patterns and is a standard benchmark for knowledge graph embedding quality.