Graph Neural Networks (GNNs) are a type of neural network architecture designed to work with data structured as graphs. Graphs are mathematical structures that describe the relationships between various entities. They consist of nodes (also called vertices) that represent the entities, and edges that represent the relationships between them.

GNNs are powerful because they can take advantage of the complex relationships in graph data. This enables them to be used in various applications like social network analysis, biological network analysis, recommendation systems, and more.

Here’s a high-level overview of how GNNs work:

1. Node Representation: Each node in the graph is represented by a feature vector.
2. Message Passing: GNNs operate by iteratively passing messages between nodes. A node’s new feature vector is computed by aggregating information from its neighbors. This process is often referred to as message passing or neighborhood aggregation.
3. Aggregation Functions: Different aggregation functions can be used to combine information from neighboring nodes, such as summation, mean, maximum, etc.
4. Update Functions: After aggregation, an update function is used to combine the aggregated information with the node’s existing feature vector, generating a new feature vector.
5. Readout Function: After several iterations of message passing, a readout function is used to generate a graph-level representation from the node-level representations. This can be used for graph classification tasks.
6. Training: GNNs are typically trained using gradient-based optimization methods, and the loss function depends on the specific task (e.g., node classification, link prediction, graph classification).

GNNs can be implemented using deep learning frameworks like TensorFlow and PyTorch. Several specialized libraries, such as DGL (Deep Graph Library) and PyTorch Geometric, have been developed to simplify working with graph neural networks.

GNNs are an active area of research, and various architectures and techniques are continually being developed to enhance their capabilities and performance.