Graphlets: a Spectral Perspective of Graph Limits

Details Graphlets: a Spectral Perspective of Graph Limits Graphlets: a Spectral Perspective of Graph Limits

2012-03-10

arxiv.org/abs/1203.2269v1

Mathematics

Combinatorics

Scientific paper

Graphlets give a spectral approach to graph limits for general graph sequences in a framework that unifies previous disparate approaches for dealing with dense graphs and sparse graphs. We will show that the convergence to graphlets under the appropriate spectral distance is equivalent to the convergence using the (normalized) cut distance. We then examine the geometry of graphlets, illustrated by examples of several families of graphlets and, in particular, graphlets with low ranks. We further discuss a number of usages of graphlets, including universal scalable bases, universal embeddings vis heat kernels and the preservation of Cheeger cuts.

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