The previous chapter established the general message passing framework, which provides a blueprint for how Graph Neural Networks operate. This chapter transitions from that abstract formulation to specific, named architectures that put these principles into practice. We will examine how different choices for the aggregation and update functions lead to models with distinct behaviors and performance characteristics.

You will learn the mechanics behind three foundational models:

• Graph Convolutional Networks (GCNs): A popular and efficient architecture that adapts the concept of convolution to graph structures through a simplified spectral approach.
• GraphSAGE: An inductive model that learns generalized aggregation functions and uses neighborhood sampling, allowing it to generate embeddings for nodes not seen during training.
• Graph Attention Networks (GATs): An architecture that incorporates masked self-attention mechanisms to assign different weights to different nodes within a neighborhood.

For each model, we will cover its mathematical formulation and discuss its primary advantages and limitations. The chapter concludes with a hands-on exercise to build a GCN from scratch, connecting the theoretical formulas directly to functional code.