Do you need to know a lot of (regular?) graph theory to get into spectral graph theory?
What are the prerequisites?
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I agree with Jack D'Aurizio. If you think you know enough Graph Theory to understand Spectral Graph Theory, grab a Spectral Graph Theory book and start reading it. (My suggestions: Read either Spectral Graph Theory by Fan R. K. Chung, or Graph Spectra by Miegham) If you dont know a graph theory concept mentioned, search it up and learn it. Here's some "prerequisites" I think you would need to know for Spectral Graph Theory.
-High Knowledge of Polyomials
-Eigenvector Values for Matrices
-Lapacian Matrices (Basic knowledge)
-Graph Variance and Invariance
Good Luck with Spectral Graph Theory