I will be working with Dr. Fiorini on describing the connections between Linear Algebra, Graph Theory, and Finite Geometry. There already exists a rich body of work regarding the connections between Linear Algebra and Graph Theory, but an equivalent body of work that also relates Finite Geometry does not exist. During my time here, I hope to establish some necessary and sufficient conditions for the existence of a projective plane within a graph and to use algebraic techniques to do so when viewing the graph is not feasable and/or possible.