New York Journal of Mathematics
NYJM Monographs, Volume 4, 2013


Svante Janson

Graphons, cut norm and distance, couplings and rearrangements

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Published: March 4, 2013
Keywords: Graph limits; graphons; cut norm; cut distance
Subject: 05C99, 28A20

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.

Author information

Department of Mathematics, Uppsala University, PO Box 480, SE-751 06 Uppsala, Sweden