Multigraph limits, unbounded kernels, and Banach space decorated graphs
  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\'avid Kunszenti-Kov\'acs, L\'aszl\'o Lov\'asz and Bal\'azs Szegedy
math.CO math.FA