There is a active area of research on generalising matrix-based methods for graph theory to the infinite case with operators. Topics of interest are generalisations of spectral graph theory and graph C*-algebras. Links to random graph theory would also be interesting to me.
What books are there on this intersection of the fields and which are advised for someone trying to get started? Some books I have found so far are
- Spectral Analysis on Graph-like Spaces (Olaf Post)
- Operator Calculus on Graphs (Rene Schott, George Stacey Staples)
- Recent Results in the Theory of Graph Spectra, Chapter 6 (D.M. Cvetkovic et. al.)