ABSTRACT
We start 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 linear algebraist in us would say, “let’s change our names and instead of calling it an array let us call it a matrix.” At first glance this may not seem like much, but recall that a matrix is an array with benefits. Among these benefits are the eigenvalues and singular values of the matrix. The eigenvalues give information about the linear transformation to which the matrix corresponds and can capture some structural properties of the graph (often with just knowing a few of the extremal eigenvalues). This provides a way to capture information about a graph with just a handful of parameters.
