The (finite, simple) graphs with the property that their adjacency matrices have spectral radius less than $2$ are precisely the simply laced Dynkin diagrams $A_n, D_n, E_6, E_7, E_8$. Similarly, the graphs with spectral radius exactly $2$ are precisely the affine simply laced Dynkin diagrams $\widetilde{A}_n, \widetilde{D}_n, \widetilde{E}_6, \widetilde{E}_7, \widetilde{E}_8$. This ties most directly into the McKay correspondence, but also to the classification of simple Lie algebras and other places where ADE classifications appear.