IMPROVING RESULTS FOR CUT AND OPERATOR NORMS ON GRAPHON

Abstract

Abstract: Graphon theory has recently begun attracting interdisciplinary research. Although the theory includes many intriguing concepts, one important aspect we often employ in network analysis is the relationship between the cut norm and operator norm of a graphon as an operator on some function spaces. This relationship is well known in the past arguments. However, the authors of the past works restricted the domain of a graphon to L∞(I). In this note, we discuss the relationship between the cut norm and operator norm of a graphon in more general situations. We improve the well-known existing inequality and enhance the accuracy of some lemma proofs.