Graphons, cut norm and distance, couplings and rearrangements
arXiv:1009.2376
Abstract
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 Lovász. We allow graphons on general probability spaces whenever possible. We also give some new results for {0,1}-valued graphons and for pure graphons.
72 pages. This version contains a new section on pure graphons and some other minor additions, including a new appendix and new references