Graph neural networks extend deep learning to data that is naturally structured as graphs, such as molecules, social networks, transportation systems and knowledge graphs. Instead of operating on fixed size vectors or grid like images, they work on nodes and edges, learning how information should flow across connections.

A central idea is message passing. Each node starts with an initial feature vector. At each layer, a node receives messages from its neighbors, aggregates them and updates its own representation. Repeating this process lets information propagate through the graph, so the final node embeddings capture both local structure and multi hop context. Variants differ in how they compute and combine messages, for example using simple averaging, learned weights or attention mechanisms that focus on the most relevant neighbors.

These models are applied to node level tasks such as classification and regression, edge level tasks such as link prediction and graph level tasks such as predicting molecular properties. In chemistry, they help design drugs and materials by encoding 3D structures and quantum properties. In physics, they model interacting particles and simulate dynamics. In recommendation and social networks they infer preferences and communities. In transportation and infrastructure they support routing, fault detection and resilience analysis.

Key research challenges include oversmoothing when many layers blur node distinctions, scalability to very large graphs, handling dynamic and temporal graphs and improving robustness and interpretability. Recent work explores hierarchical pooling, positional encodings, equivariant architectures, self supervision and combining graphs with text and images, expanding the range and reliability of graph based learning.