Spectral graph theory in a nutshell
Spectral graph theory is the study of the spectrum (set of eigenvalues) of certain matrices associated with graphs. It has applications in the analysis of networks in, for example, the social and biological sciences. In this talk, we define the adjacency matrix of a graph and use it to define the normalized Laplacian matrix of a graph. We then study the spectrum of this normalized Laplacian and its relation to some global properties of the associated graph.