UGC: Universal Graph Coarsening

In the era of big data, graphs have emerged as a natural representation of 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 the basic statistics of the graphs, such as spectral properties and ϵ-similarity in the coarsened graph. This ensures that downstream processes are more efficient and effective.