# Twice-Ramanujan Sparsifiers

SIAM Review, pp. 315-334, 2014.

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Abstract:

We prove that every graph has a spectral sparsifier with a number of edges linear in its number of vertices. As linear-sized spectral sparsifiers of complete graphs are expanders, our sparsifiers of arbitrary graphs can be viewed as generalizations of expander graphs. In particular, we prove that for every $d>1$ and every undirected, we...More

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