Spectral and Algebraic Graph Theory (cs-www.cs.yale.edu)

I saw a link posted to a rather short note on graphs and linear algebra. I thought I'd better do some advertising for the real deal!

Took Spielman's spectral graph theory class back in the day. Was really cool to see the professor engage with students on open questions that pushed at the boundaries of research!

This is also an excellent book on the subject: https://bookstore.ams.org/cbms-92