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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.

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  • $\begingroup$ I am not familiar with the topic but the general recommendation is: search for scientific papers (google scholar for example) on the topic. If it's well researched, you will find some useful information, and many references, including possibly to books $\endgroup$ – Yuriy S Jun 8 '18 at 12:36

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