Universality and Random Matrix Theory

It is worth delving deeper into the eigenvalues of the matrices associated with CSNs, specifically into the correlations between these eigenvalues, because such correlations can reveal a lot about the topology of the underlying space, as well as the similarities between molecules. But there are in-built correlations between the eigenvalues of even random networks. Which correlations are intrinsic to the structure of the space and the chosen similarity metric, and which of them reveal non-trivial similarity relationships between molecules? These re non-trivial questios, but random matrix theory (RMT) can provide some clues. In this chapter, we will continue discussion of the eigenvalues of matrices associated with graphs, from the standpoint of random matrix theory.