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One way to store information about a graph is by an array with entries indexed by pairs of vertices with each entry giving information about a 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, which 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 this can capture some structural properties of the graph (often with just knowing a few of the extremal eigenvalues). This provides a way to obtain information about a graph with just a handful of parameters. We will explore several different possible matrices and look at some of the information that we can, and in some cases cannot, learn by studying the eigenvalues.