Benchmarking parallel eigen decomposition for residuals analysis of very large graphs

Graph analysis is used in many domains, from the social sciences to physics and engineering. The computational driver for one important class of graph analysis algorithms is the computation of leading eigenvectors of matrix representations of a graph. This paper explores the computational implications of performing an eigen decomposition of a directed graph´s symmetrized modularity matrix using commodity cluster hardware and freely available eigensolver software, for graphs with 1 million to 1 billion vertices, and 8 million to 8 billion edges. Working with graphs of these sizes, parallel eigensolvers are of particular interest. Our results suggest that graph analysis approaches based on eigen space analysis of graph residuals are feasible even for graphs of these sizes.