Triangle-aware Spectral Sparsifiers and Community Detection

Triangle-aware graph partitioning has proven to be a successful approach to finding communities in real-world data [8, 40, 51, 54]. But how can we explain its empirical success? Triangle-aware graph partitioning methods rely on the count of triangles an edge is contained in, in contrast to the well-established measure of effective resistance [12] that requires global information about the graph.