**Les Graphes dans la Mecenique Quantique**

All fundamental particles in the universe come in two types:
fermions and bosons. The former category contains electrons, protons,
and neutrons, and forbids two particles from occupying the same quantum
state (the Pauli exclusion principle); the latter category, which
contains photons and other force-carrying particles, has no such
restriction. When bosons and fermions are confined in lattices, such as
in solid-state systems, the equations of motion can be phrased in terms
of the adjacency matrix of an undirected and generally weighted graph.
The properties of these quantum many-particle systems can therefore be
analyzed in terms of graph theory. I will discuss these relationships,
and show that by using graph theory, it is possible to obtain a more
efficient determination of the eigenstates (and therefore the properties
and dynamics) of interesting physical systems.