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I don't know how proof heavy this course is and it is not specialized on graphs: "Computational Science and Engineering I" -- Gilbert Strang (MIT)

https://ocw.mit.edu/courses/18-085-computational-science-and...

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The textbook for this course is probably one of the finest Strang ever wrote. It's also worth looking at the original edition of the textbook, which was called "Introduction to Applied Mathematics" and has a much more thorough treatment of the parallels between matrices, graphs, and differential operators, and their use in optimization problems. CSE is much more practical for solving actual scientific computing problems, though, even if I find the layout somewhat less beautiful.

oh my, thanks! Ed 1 is the exact book i wanted

Were you able to find a copy? I found this on archive.org -- https://archive.org/details/introductiontoap0000stra/page/n9...

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