Graph Neural Networks (GNNs) Cheat Sheet

Updated 2026-05-02

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Graph Neural Networks represent a fundamental advancement in deep learning, enabling neural networks to directly process graph-structured data where entities (nodes) and their relationships (edges) carry semantic meaning. Unlike traditional neural networks that operate on grid-like structures (images, sequences), GNNs exploit the topology and connectivity patterns inherent in graphs through message passing — iteratively aggregating information from neighboring nodes to update node representations. GNNs have become the standard architecture for learning from networks in molecular chemistry, social systems, knowledge graphs, and any domain where relationships between entities are as important as the entities themselves. A critical insight: most GNN architectures are permutation equivariant (node order doesn't matter) yet often limited by the Weisfeiler-Leman test in their ability to distinguish certain graph structures.

What This Cheat Sheet Covers

This topic spans 19 focused tables and 146 indexed concepts. Below is a complete table-by-table outline of this topic, spanning foundational concepts through advanced details.

Table 1: Core GNN Layer ArchitecturesTable 2: Message Passing Framework ComponentsTable 3: Graph Pooling MethodsTable 4: GNN Training TasksTable 5: PyTorch Geometric (PyG) Core APITable 6: Deep Graph Library (DGL) APITable 7: Knowledge Graph EmbeddingsTable 8: Molecular Graph ApplicationsTable 9: GNN Normalization TechniquesTable 10: Graph Data AugmentationTable 11: Regularization and Dropout MethodsTable 12: Advanced GNN ArchitecturesTable 13: GNN Explainability MethodsTable 14: Training Techniques and OptimizationTable 15: GNN Challenges and SolutionsTable 16: Self-Supervised Learning on GraphsTable 17: Datasets and BenchmarksTable 18: Inductive vs. Transductive LearningTable 19: Graph Laplacian and Spectral Methods

Table 1: Core GNN Layer Architectures

These are the workhorse layers you reach for first, and they differ mainly in how a node decides which neighbors to listen to. GCN weights them by degree, GAT learns attention over each edge, GraphSAGE samples a fixed neighborhood so it scales and generalizes to unseen nodes, and GIN uses injective sum aggregation to squeeze out the most expressive power within the 1-WL limit.

Architecture	Example	Description
Graph Convolutional Network (GCN)	`GCNConv(in_channels, out_channels)` `h_i' = σ(∑_{j∈N(i)} (1/√(d_i·d_j)) W h_j)`	• Spectral-inspired layer using symmetric normalization of the adjacency matrix • aggregates neighbor features weighted by node degree • foundational but prone to oversmoothing
Graph Attention Network (GAT)	`GATConv(in_channels, out_channels, heads=8)` `α_ij = softmax(LeakyReLU(a^T[Wh_i \|\| Wh_j]))`	• Learns attention weights $\alpha_{ij}$ for each edge to determine neighbor importance • supports multi-head attention for richer representations • handles heterogeneous neighborhoods better than GCN
GraphSAGE	`SAGEConv(in_channels, out_channels, aggr='mean')` `h_i' = σ(W·CONCAT(h_i, AGG({h_j : j∈N(i)})))`	• Inductive learning via neighborhood sampling (fixed-size subsets) • aggregates via mean/max/LSTM • scales to unseen nodes • critical for large graphs
Graph Isomorphism Network (GIN)	`GINConv(MLP)` `h_i' = MLP((1+ε)·h_i + ∑_{j∈N(i)} h_j)`	• Provably maximally expressive within 1-WL test hierarchy • uses injective sum aggregation with learnable $\epsilon$ • distinguishes more graph structures than GCN/GAT

Table 1: Core GNN Layer Architectures

Architecture	Example	Description
Graph Convolutional Network (GCN)	`GCNConv(in_channels, out_channels)` `h_i' = σ(∑_{j∈N(i)} (1/√(d_i·d_j)) W h_j)`	• Spectral-inspired layer using symmetric normalization of the adjacency matrix • aggregates neighbor features weighted by node degree • foundational but prone to oversmoothing
Graph Attention Network (GAT)	`GATConv(in_channels, out_channels, heads=8)` `α_ij = softmax(LeakyReLU(a^T[Wh_i \|\| Wh_j]))`	• Learns attention weights $\alpha_{ij}$ for each edge to determine neighbor importance • supports multi-head attention for richer representations • handles heterogeneous neighborhoods better than GCN
GraphSAGE	`SAGEConv(in_channels, out_channels, aggr='mean')` `h_i' = σ(W·CONCAT(h_i, AGG({h_j : j∈N(i)})))`	• Inductive learning via neighborhood sampling (fixed-size subsets) • aggregates via mean/max/LSTM • scales to unseen nodes • critical for large graphs
Graph Isomorphism Network (GIN)	`GINConv(MLP)` `h_i' = MLP((1+ε)·h_i + ∑_{j∈N(i)} h_j)`	• Provably maximally expressive within 1-WL test hierarchy • uses injective sum aggregation with learnable $\epsilon$ • distinguishes more graph structures than GCN/GAT