Graph Machine Learning

Vertices, edges, degree, paths, cycles, connectivity, bipartite and directed graphs, trees and DAGs.

Assumes: Graph Representations

Adjacency, degree and incidence matrices, edge indices, node and edge features, and sparse formats.

Assumes: Graph Theory Refresher

Unnormalised and normalised Laplacians, the quadratic form, and what the null space encodes.

Assumes: Representing Graphs for Learning · Quadratic Forms and Definiteness

Laplacian eigenvalues, algebraic connectivity, the Fiedler vector and spectral partitioning.

Assumes: The Graph Laplacian

Degree, closeness, betweenness and eigenvector centrality, computed on a worked graph.

Assumes: Representing Graphs for Learning

The random surfer model, the power iteration, damping, and handling dangling nodes.

Assumes: Centrality Measures · Markov Chains

Mutual reinforcement of hub and authority scores, and the contrast with PageRank.

Assumes: PageRank

Modularity, the Louvain and Leiden methods, label propagation and Girvan–Newman.

Assumes: Spectral Graph Theory

Common neighbours, Jaccard, Adamic–Adar, SimRank and personalised PageRank proximity.

Assumes: PageRank

Random walks as sentences, skip-gram over graphs, and the shallow-embedding paradigm.

Assumes: Node Similarity and Proximity · word2vec: CBOW and Skip-Gram

Biased second-order walks, the p and q parameters, and the homophily/structural-equivalence trade-off.

Assumes: DeepWalk

Aggregate, update and readout as a unifying abstraction for every GNN in this module.

Assumes: node2vec · Backpropagation

The GCN layer, symmetric normalisation, self-loops, and a full numeric forward pass on a small graph.

Assumes: The Message Passing Framework

Graph Fourier transform, Chebyshev polynomial filters, and the first-order approximation that yields GCN.

Assumes: Graph Convolutional Networks · Spectral Graph Theory

Neighbour sampling, mean/pool/LSTM aggregators, and inductive generalisation to unseen nodes.

Assumes: Graph Convolutional Networks

Learned attention coefficients over neighbours, multi-head attention on graphs, and interpretability.

Assumes: GraphSAGE · The Attention Mechanism

The Weisfeiler–Lehman test, what message passing provably cannot distinguish, and GIN's injective aggregation.

Assumes: Graph Attention Networks

Sum, mean and max readout, DiffPool, Top-K pooling, and graph-level prediction.

Assumes: GIN and GNN Expressiveness

Why deep GNNs collapse node representations, and the residual, jumping-knowledge and PairNorm fixes.

Assumes: Graph Pooling and Readout

Neighbour explosion, layer-wise and subgraph sampling, Cluster-GCN and GraphSAINT.

Assumes: Over-Smoothing and Depth in GNNs

Multiple node and edge types, metapaths, R-GCN and heterogeneous attention.

Assumes: Scalable GNN Training

Triples, TransE, DistMult, ComplEx and RotatE, and knowledge-graph completion.

Assumes: Heterogeneous and Multi-Relational Graphs

Snapshot and continuous-time formulations, temporal message passing and TGN.

Assumes: Knowledge Graphs and Embeddings

Heuristic scores, encoder–decoder formulations, negative sampling and ranking evaluation.

Assumes: Graph Attention Networks

Full attention over nodes, structural and positional encodings for graphs, and scalability limits.

Assumes: Link Prediction · The Transformer Architecture

Recommendation, molecular property prediction, fraud detection, traffic forecasting and physics simulation.

Assumes: Link Prediction