On derivatives of graphon parameters

Abstract

We give a short elementary proof of the main theorem in the paper "Differential calculus on graphon space" by Diao et al. (JCTA 2015), which says that any graphon parameters whose $(N+1)$-th derivatives all vanish must be a linear combination of homomorphism densities $t(H,-)$ over graphs $H$ on at most $N$ edges.

4 pages

References in corpus (1)

• Differential Calculus on Graphon Space

Cited by in corpus (1)

• Gradient flows on graphons: existence, convergence, continuity equations