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We initiate a principled study of graph densification. Given a graph G the goal of graph densification is to come up with another graph H that has significantly more edges than G but nevertheless approximates G well with respect to some set of test functions. In this paper we focus on the case of cut and spectral approximations. As it turns out graph densification exhibits rich connections to a set of interesting and sometimes seemingly unrelated questions in graph theory and metric embeddings.doi:10.1145/2090236.2090266 dblp:conf/innovations/HardtST12 fatcat:hkonhol52rdvfbgsxiwvisj2g4