The generalized graph matrix Gamma(x,v) (Estrada, E. Chem. Phys. Lett. 2001, 336, 247) is shown to encompass several of the applications of graph theory in physical chemistry in a more compact and effective way. it defines several n-Euclidean graph metrics, which simulate a graph defolding by changing the exponent v from 0 to 0.5 in a continuous way. This matrix is included in the formalism of the Huckel molecular orbital approach by considering that the resonance integrals between nonneighbor atoms are a function of the topological distance in terms of beta. In doing so, the isospectrality between graphs disappears by changing the x parameter in this matrix as a consequence of considering the interactions between nonneighbor atoms. The Gamma(x,v) matrix permits several of the "classical" topological indices to be (re)defined using only one graph invariant. These indices include the connectivity index, Balaban J index, Zagreb indices, Wiener index, and Harary indices, which are represented in an 8-dimensional space of parameters to show their similarities and differences. The indices can be optimized to describe physicochemical properties by changing in a systematic way the parameters of the generalized graph matrix and vectors. We show here how a dramatic improvement is obtained by optimizing the Wiener index for describing octane boiling points (from R = 0.53 to R = 0.94), also providing a structural interpretation of the model found.