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Graph disaggregation is a technique used to address the high cost ofcomputation for power law graphs on parallel processors. The few high-degreevertices are broken into multiple small-degree vertices, in order to allow formore efficient computation in parallel. In particular, we consider computationsinvolving the graph Laplacian, which has significant applications, includingdiffusion mapping and graph partitioning, among others. We prove resultsregarding the spectral approximation of the Laplacian of the original graph bythe Laplacian of the disaggregated graph. In addition, we construct analternate disaggregation operator whose eigenvalues interlace those of theoriginal Laplacian. Using this alternate operator, we construct a uniformpreconditioner for the original graph Laplacian.

On the Approximation of Laplacian Eigenvalues in Graph Disaggregation