Book recommendations for spectral graph theory

Question

I am working on a Natural Sciences related project, which involves graph theory. I have calculated the Laplacian and Adjacency spectra of my graphs and now have to interpret it.

However, I am not a mathematician and most books, that I have found, have quite a lot of proofs and theorems, which are indeed interesting, but not necessary for the interpretation of a spectra.

Maybe someone could recommend a book or an article that deals with the interpretation of the spectra? I am mostly interested in overall connectivity, topology, cycles, small-world or random structures and properties like that determination from the spectra of a graph.

Answer 1

1. Spectra of graphs: theory and applications by Dragos M. Cvetkovic, Michael Doob, Horst Sachs;
2. http://www.math.ucsd.edu/~fan/research/revised.html
3. https://link.springer.com/book/10.1007/978-1-4471-6569-9
4. https://www.cambridge.org/core/books/eigenspaces-of-graphs/3EB0B8BE4189DDE43005E311A5331523
5. https://www.elsevier.com/books/recent-results-in-the-theory-of-graph-spectra/cvetkovic/978-0-444-70361-3

You can go through the book by R.B. Bapat, the third link.

Answer 2

How about these?

Introduction to graph theory

Introduction to Topology