… that GΔ is a cut sparsifier of GΔ, G would be a motif cut sparsifier of G. It is a seemingly natural
approach to try to use triangle weighted graphs to obtain triangle sparsifiers. However, we …

… Here, we focus on the triangle motif that plays an important role in social networks [… sparsifiers
find applications in solving Laplacian systems [? ], while can be also used to speed-up cut …

… Motif Cut Sparsifiers … Spectral Hypergraph Sparsifiers of Nearly Linear Size …

… An Optimal Space Lower Bound for Approximating MAX-CUT … Motif Cut Sparsifiers …

… Finally, we investigate cut and spectral sparsifiers with respect to triangle counting and …
the SpielmanSrivastava spectral sparsifier [46] and the the Benczúr-Karger cut sparsifier [8, 9] …

… sparsifiers paper [74], and in Chapter 6 of [29]. We next review algorithms for dynamically
maintaining cut sparsifiers … maintains a (1+𝜖)-cut sparsifier 𝐻 of 𝐺 whp while support insertions/…

… In fact, we show that even outputting a weaker cut sparsifier requires the same number … motif
clustering, which is a graph clustering method that is based on higherorder patterns or motifs…

… For instance, Benczúr and Karger introduced the notion of cut sparsification to accelerate cut
… notion of a cut sparsifier by introducing the more general notion of a spectral sparsifier [52]. …

… sparsifier approximates the quadratic form of the Laplacian of a graph. Note that a spectral
sparsifier is also a cut sparsifier… , the notions of cut sparsifier and spectral sparsifier have been …

… Motif Cut Sparsifiers 389 Michael Kapralov (EPFL, Switzerland), Mikhail Makarov (EPFL,
Switzerland), Sandeep Silval (MIT, USA), Christian Sohler (University of Cologne, Germany), …