  The object of this work is the systematical study of a certain type of
generalized Cartan matrices associated with the Dynkin diagrams that
characterize Cartan-Lie and affine Kac-Moody algebras. These generalized
matrices are associated to graphs which arise in the study and classification
of Calabi-Yau spaces through Toric Geometry. We focus in the study of what
should be considered the generalization of the affine exceptional series
$E_{6,7,8}^{(1)}$ Kac-Moody matrices. It has been conjectured that these
generalized simply laced graphs and associated link matrices may characterize
generalizations of Cartan-Lie and affine Kac-Moody algebras.
