Abstract: Quantum physics has revolutionized the way we understand our world. Since the beginning of the 20th century, beautiful mathematics has been devised and implemented in order to achieve such success. This talk intends to give an overview of a discretized model of quantum mechanics: the Schrödinger equation on graphs. We will use the combinatorial graph Laplacian to describe certain properties of finite graphs such as topological invariants, number of generalized walks and entropy. No prior knowledge of physics or graph theory will be assumed.