Graphons, cut norm and distance, couplings and rearrangements

By Svante Janson. 2010

144 citations recorded by the source corpus.

We give a survey of basic results on the cut norm and cut metric for graphons (and sometimes more general kernels), with emphasis on the equivalence problem. The main results are not new, but we add various technical complements, and a new proof of the uniqueness theorem by Borgs, Chayes and Lov\'asz. We allow graphons on general probability spaces whenever possible. We also give some new results for {0,1}-valued graphons and for pure graphons.

Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/62884cf451533aa69534a15a0cbef3108bfdd49d