Global graph features unveiled by unsupervised geometric deep learning

Graphs are used to model complex relationships in various domains, such as interacting particles or neural connections within a brain. Efficient analysis and classification of graphs pose significant challenges due to their inherent structural complexity and variability. Here, an approach is presented to address these challenges through the development of a Graph Autoencoder Uncovering Descriptive Information (GAUDI). GAUDI effectively summarizes graph structures while preserving important topological details through multiple hierarchical pooling steps. This enables the extraction of physical parameters describing the graphs. The performance of GAUDI is demonstrated across diverse graph data originating from complicated systems, including the classification of protein assembly structures from single--molecule localization microscopy data, as well as the analysis of collective behavior and correlations between brain connections and age. This approach holds great promise for examining diverse systems, enhancing our comprehension of various forms of graph data.