• Corpus ID: 238419338

Laplacians on infinite graphs: discrete vs continuous

  title={Laplacians on infinite graphs: discrete vs continuous},
  author={Aleksey Kostenko and Noema Nicolussi},
There are two main notions of a Laplacian operator associated with graphs: discrete graph Laplacians and continuous Laplacians on metric graphs (widely known as quantum graphs). Both objects have a venerable history as they are related to several diverse branches of mathematics and mathematical physics. The existing literature usually treats these two Laplacian operators separately. In this overview, we will focus on the relationship between them (spectral and parabolic properties). Our main… 


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  • U. Feige
  • Zeta and 𝐿-functions in Number Theory and Combinatorics
  • 2019
With every graph (or digraph) one can associate several different matrices. We have already seen the vertex-edge incidence matrix, the Laplacian and the adjacency matrix of a graph. Here we shall