Diversity Curves for Graph Representation Learning
For researchers in graph representation learning, this work provides a novel, interpretable, and efficient embedding that addresses the challenge of comparing graphs of varying sizes, with demonstrated utility in diverse applications.
The paper introduces diversity curves, a graph-level representation that tracks structural diversity across coarsening levels, enabling interpretable and scalable comparison of graphs with different sizes. The method outperforms baselines in clustering, visualization, and distinguishing graph geometries across multiple domains.
Graph-level representations are crucial tools for characterising structural differences between graphs. However, comparing graphs with different cardinalities, even when sampled from the same underlying distribution, remains challenging. Unsupervised tasks in particular require interpretable, scalable, and reliable size-aware graph representations. Our work addresses these issues by tracking the structural diversity of a graph across coarsening levels. The resulting graph embeddings, which we denote diversity curves, are interpretable by construction, efficient, and directly comparable across coarsening hierarchies. Specifically, we track the spread of graphs, a novel isometry invariant that is inherently well-suited for encoding the metric diversity and geometry of graphs. We utilise edge contraction coarsening and prove that this improves expressivity, thus leading to more powerful graph-level representations than structural descriptors alone. Demonstrating their utility over a range of baseline methods in practice, we use diversity curves to (i) cluster and visualise simulated graphs across varying sizes, (ii) distinguish the geometry of single-cell graphs, (iii) compare the structure of molecular graph datasets, and (iv) characterise geometric shapes.