Introduction

In this topic, we study Graph Neural Networks (GNN), whose main objective is to learn from data that can be naturally represented as graphs. A graph is a structure formed by nodes (vertices) and edges that describe relationships or interactions between entities. This form of representation is especially suitable for numerous real-world problems, in which the connections between elements are as important as the elements themselves.

Graphs appear implicitly in many everyday domains. In social networks, for example, each user can be modeled as a node and friendship, following, or interaction relationships as edges. Furthermore, attributes or characteristics can be associated with each node, such as salary range, age, geographic location, occupation, or demographic variables. These characteristics, together with the connection structure, allow building models that better capture the dynamics and organization of the social network than if users were considered in isolation.

Similarly, an image can be interpreted as a graph in which each pixel acts as a node connected to its neighboring pixels (in a 4, 8, or wider neighborhood), and where the intensity or color vector (for example, in RGB format) is used as node attributes. This graph perspective allows applying graph-based processing techniques to visual problems, establishing a bridge between computer vision and graph learning.

There are also graph representations that are especially relevant in scientific and industrial fields. A paradigmatic case is that of molecules, where atoms are modeled as nodes and chemical bonds as edges. This type of representation has been key in developments such as AlphaFold, presented by Google DeepMind, for protein folding, or in multiple works on drug discovery and computational chemistry. Another example is offered by systems like Google Maps, where intersections and points of interest can be considered nodes, and roads or connections between them, edges; on this structure, problems such as traffic prediction, travel time estimation, or optimal route calculation are formulated.

Throughout the topic, we will see how to preprocess and transform heterogeneous data to represent them as graphs suitable for training neural models. We will analyze how to explicitly define nodes, edges, and their attributes, and how to construct data structures compatible with modern deep learning libraries for graphs.

A central objective is to understand how to implement a graph from scratch and how to apply different variants of graph neural networks to it. Special emphasis is placed on GNN based on graph convolutions (Graph Convolutional Networks, GCN), which generalize the idea of classical convolution to non-Euclidean domains. In this framework, each node updates its representation by aggregating information from its neighbors according to a message passing scheme, which allows capturing local and global patterns in the graph structure.

In addition to graph convolutions, we also study attention mechanisms in graphs (Graph Attention Networks, GAT and variants). These methods assign differentiated weights to connections between nodes, allowing the network to learn which neighbors it should pay more attention to depending on the context and task. This approach is especially useful when the importance of relationships is not homogeneous or when a finer interpretation of interactions between nodes is desired.

The techniques described are applied both to images modeled as graphs and to other types of data structured in networks, demonstrating the versatility of GNNs to address problems of node classification, link prediction, whole graph classification, and other related tasks.

For practical implementation, we will use the PyTorch Geometric library, a specialized framework that extends PyTorch with data structures and optimized operations for deep learning on graphs. PyTorch Geometric facilitates the definition of graphs, the construction of graph convolution and attention layers, and the training of complex models on large collections of graphs or large-scale graphs.