Heat equation on a graph Laplacian

Question

I would like to start with considering the time-dependent heat equation on a connected graph. To start, I will need to model it respect to time discretization. I mean I have to write something like: $$A T^{k+1} = B T^k + Cf^k$$ where the initial time is given and the time step is assumed to be fixed. First, I have to determine the matrix A, B, and C and write down in what form they will be.

Would you please let me know if you know some references or have some comments on this topic?

Answer 1

Try this document

PDE Approaches to Graph Analysis (Justin Solomon, Stanford)