There are many ways to represent a graph as a matrix; the adjacency and Laplacian matrices are two examples. Once the graph “becomes” a matrix, it takes on the properties of that matrix. It has a determinant, a rank, and eigenvalues. The eigenvalues of the adjacency matrix has been the topic of over 1,000 research papers during the past several decades. But the less-well-known Laplacian matrix has better algebraic properties. In this talk I will describe the Laplacian matrix and a little of its history including a result of mine connecting it with the classical area of integral quadratic forms.