I was hoping someone would recommend a good book as an introduction to differential equations on Graphs or networks. So this would include both ODEs and PDEs. After looking around I have not been able to find an comprehensive treatment. In Fan Chung's book on spectral graph theory, there is a chapter on the heat kernel on graphs--but did not find any mention of the wave equation or Schrodinger equation on graphs. Cvetkovic and the Brouwer&Haemers book don't mention PDEs at all. I have not really found any treatments of ODEs on graphs at all.
I understand that this type of topic spans a number of disciplines. So for the spectral graph theory connection you need a stronger grasp of differential topology and Riemann geometry. But I was hoping that someone could point out some good starting points on this topic.