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References: GNN Foundations: Message Passing and GCN

  1. Graph Neural Network - Wikipedia - Covers the history and taxonomy of graph neural networks, from early recurrent formulations through modern message-passing architectures. A reliable entry point for situating GCN within the broader GNN family.

  2. Laplacian Matrix - Wikipedia - Defines the combinatorial, normalized, and symmetric normalized Laplacians with worked examples on small graphs. Essential background for understanding the spectral convolution derivation in this chapter.

  3. Spectral Graph Theory - Wikipedia - Explains the relationship between a graph's eigenspectrum and its structural properties, including connectivity, clustering, and random walks. Provides the mathematical foundation for why convolution in the spectral domain is well-defined.

  4. Deep Learning on Graphs - Yao Ma and Jiliang Tang - Cambridge University Press - A graduate-level textbook dedicated to graph deep learning; Chapters 2–4 cover spectral and spatial GNNs with full derivations. The treatment of GCN, ChebConv, and MPNN closely parallels this chapter's content.

  5. Graph Representation Learning - William L. Hamilton - Morgan & Claypool (Synthesis Lectures on AI and ML) - A concise monograph covering node embeddings through GNNs; freely available from the author's website. Chapter 4 derives GCN from first principles and provides one of the clearest expositions of the spectral-to-spatial approximation chain.

  6. Semi-Supervised Classification with Graph Convolutional Networks (Kipf & Welling, 2017) - arXiv - The original GCN paper; derives the layer-wise propagation rule from a first-order Chebyshev approximation of spectral graph convolutions. Reading Sections 2.1–2.2 alongside this chapter's derivation is the most direct way to understand the renormalization trick.

  7. Neural Message Passing for Quantum Chemistry (Gilmer et al., 2017) - arXiv - Introduces the Message Passing Neural Network (MPNN) framework that unifies GCN, GG-NN, and interaction networks under a single message–aggregate–update formalism. The notation used in this chapter follows MPNN directly.

  8. PyTorch Geometric MessagePassing Documentation - PyTorch Geometric Docs - Official tutorial for implementing custom GNN layers using PyG's MessagePassing base class. Explains the propagate, message, aggregate, and update hooks that map one-to-one onto the MPNN framework covered in this chapter.

  9. Stanford CS224W: Machine Learning with Graphs — Lecture 6: Graph Neural Networks - Stanford CS224W - Lecture slides and notes covering GCN, the message passing framework, and spatial vs. spectral convolutions; used in Stanford's flagship graph ML course. Provides alternative derivations and additional intuition that complement this chapter's treatment.

  10. GCN on Papers With Code - Papers With Code - Aggregates benchmark results for GCN across node classification datasets including Cora, Citeseer, and ogbn-arxiv, with links to reproducible implementations. Useful for comparing the baseline numbers cited in this chapter's benchmark table against the current state of the field.