The connections between graph theory and linear algebra, and between linear algebra and ecology, are well-established.  There is also a small but growing body of literature built around applications of graph theory to ecology: one such application is a technique known as demographic loop analysis. In this talk I will describe recent work in loop analysis in which graph theory, linear algebra, and ecology come together in a beautiful and surprising way.  This talk should be accessible to anyone with a basic undergraduate background in calculus and linear algebra.