Multigraph limits, unbounded kernels, and Banach space decorated graphs

Abstract

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.

35 pages

References in corpus (1)

• An $L^p$ theory of sparse graph convergence I: limits, sparse random graph models, and power law distributions

Cited by in corpus (2)

• Limits of discrete distributions and Gibbs measures on random graphs
• Priors on exchangeable directed graphs