UGC: UNIVERSAL GRAPH COARSENING

Mohit Kataria, Sandeep Kumar, Jayadeva Jayadeva

Primary Area: learning on graphs and other geometries & topologies

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Keywords: Graph Coarsening, Graph Neural Networks, Locality Sensitive Hashing, Graph Learning

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TL;DR: Our framework efficiently coarsen down a large graph to a smaller graph in linear time, accommodating both homophilic and heterophilic graph data.

Abstract: In the era of big data, graphs have emerged as a natural representation for intricate relationships. However, graph sizes often become unwieldy, leading to storage, computation, and analysis challenges. A crucial demand arises for methods that can effectively downsize large graphs while retaining vital insights. Graph coarsening seeks to simplify large graphs while maintaining essential features. Most published methods are suitable for homophilic datasets, limiting their universal use. We propose Universal Graph Coarsening (UGC), a framework equally suitable for homophilic and heterophilic datasets. UGC integrates node attributes and adjacency information, leveraging the dataset's heterophily factor and is a first ever linear time-complexity framework. Results on benchmark datasets demonstrate that UGC preserves spectral similarity while coarsening. In comparison to state of the art methods, UGC is 4x to 15x faster, has lower eigen-error, and yields superior performance on downstream processing tasks even at 70\% coarsening ratios.

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Submission Number: 6082