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Graph Neural Networks — Learning on Graph Structures

Expert TopicsGraph ML🟢 Free Lesson

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Advanced Topics

Graph Neural Networks — Learning from Connections and Relationships

Explore graph neural networks (GNNs) for learning on structured data with complex relationships. Perfect for social networks, molecular analysis, and recommendation systems.

  • Message Passing — How nodes aggregate information from neighbors

  • Graph Convolutional Networks — The foundational GNN architecture

  • Graph Attention Networks — Learning which connections matter most

"Everything is connected, and those connections are where the real learning happens."

Graph Neural Networks — Complete Guide

GNNs learn from graph-structured data — social networks, molecules, knowledge graphs.


Why GNNs?

Graph Data Structure

Graph-Structured Data ExamplesSocial NetworkABCDMoleculeOHHH₂O: Atoms=nodes, Bonds=edgesCitation NetworkP1P2P3P4Papers=nodes, Citations=edgesGraph Definition: G = (V, E)V = {v₁, v₂, ..., v₅} : Set of nodes (vertices)E = {(vᵢ¢, v⊥) : vᵢ¢, v⊥ ∈ V} : Set of edges (connections)Node features: X ∈ ℝ^{N×d}, Adjacency: A ∈ {0,1}^{N×N}

Message Passing

Where:

  • = node v's representation

  • = neighbors of v

Message Passing Visualization

Message Passing in GNNsStep 1: Send Messagesvu₁u₂u₃uâ‚„m_u = MSG(h_u)Step 2: Aggregate Messagesva_v = AGGREGATE({m_u})e.g., sum, mean, maxΣ m_u / |N(v)|Step 3: Update Nodevh_v' = UPDATE(h_v, a_v)e.g., MLP + ReLUσ(W · [h_v || a_v])Process repeats for K layers: each node aggregates from K-hop neighborsMore layers = larger receptive field (but risk of over-smoothing)

GCN (Graph Convolutional Network)

GCN Architecture

Graph Convolutional Network (GCN) ArchitectureInput Graph1234X ∈ ℝ^{4×3}A ∈ {0,1}^{4×4}GCN Layer 1H' = σ(D̃^{-½}σD̃^{-½}HW)Aggregate neighborsTransform featuresApply activationGCN Layer 2H'' = σ(D̃^{-½}σD̃^{-½}H'W')2-hop aggregationRicher representationsWider receptive fieldOutputNode embeddingsH^{(K)} ∈ ℝ^{N×d}For node classificationor graph-level tasksEach layer: aggregate from 1-hop neighbors. K layers = K-hop neighborhood.

GNN Variants

GCN (Graph Convolutional Network):

  • Spectral-based

  • Averaging neighbor features

  • Simple and effective

GraphSAGE:

  • Sample neighbors (scalable)

  • Multiple aggregation functions

  • Inductive (works on new nodes)

GAT (Graph Attention Network):

  • Attention over neighbors

  • Learn which neighbors matter

  • More expressive than GCN

GNN Variants Comparison

GNN Variants: GCN vs GraphSAGE vs GATGCNGraph Convolutional Network• Fixed neighborhood• Mean aggregation• Transductive (needs full graph)• Spectral theory foundationBest for: Small-medium graphsComplexity: O(|E|·d²)GraphSAGESample and AggreGatE• Neighbor sampling• Mean/Max/LSTM aggregation• Inductive (new nodes ok)• Scalable to large graphsBest for: Large graphs, graphsComplexity: O(K·|S|·d²)GATGraph Attention Network• Attention over neighbors• Weighted aggregation• Multi-head attention• More expressive than GCNBest for: Heterogeneous graphsComplexity: O(|E|·d²)All share the message-passing paradigm but differ in aggregation strategy

Key Takeaways


What to Learn Next

-> Neural Networks Fundamentals — Perceptrons to Deep Learning

Learn about neural networks fundamentals — perceptrons to deep learning.

-> Convolutional Neural Networks — Complete Guide for Vision

Learn about convolutional neural networks — complete guide for vision.

-> Transformers — Attention Is All You Need Complete Guide

Learn about transformers — attention is all you need complete guide.

-> Clustering — K-Means, DBSCAN, Hierarchical Complete Guide

Learn about clustering — k-means, dbscan, hierarchical complete guide.

-> Recommendation Systems — Collaborative and Content-Based Filtering

Learn about recommendation systems — collaborative and content-based filtering.

-> ML System Design — Architecture and Production Patterns

Learn about ml system design — architecture and production patterns.

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