We present a construction that allows us to define a limit object of Banach space decorated graph sequences in a generalized homomorphism density sense. This general functional analytic framework provides a universal language for various combinatorial limit notions. In particular it makes it possible to assign limit objects to multigraph sequences that are convergent in the sense of node-and-edge homomorphism numbers, and it generalizes the limit theory for graph sequences with compact decorations.
D. Kunszenti-Kovács, L. Lovász, B. Szegedy: Multigraph limits, unbounded kernels, and Banach space labeled graphs, Journal of Functional Analysis 282 (2) (2022), Research Paper No. 109284 (online)