On derivatives of graphon parameters

Published 27 May 2015 in math.CO and math.FA | (1505.07448v3)

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.

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