ABSTRACT
This chapter starts by noting that one way to store information about a graph is by an array with entries indexed by pairs of vertices and the entry then giving information about some relationship between the pair. The eigenvalues give information about the linear transformation to which the matrix corresponds and can capture some structural properties of the graph. This provides a way to capture information about a graph with just a handful of parameters. Spectral graph theory is the exploration of how much information we can find about the structure of the graph based on the eigenvalues of the graph. There are many possible ways to associate a graph to a matrix. The three primary elements that have been used to define the entries of the matrix are: the degree of the vertices; the adjacency indicator for a pair of vertices; and the minimum distance between pairs of vertices.
