The notions of vertex energy and centrality measures are significant graph invariants that describe the contribution of individual vertices to the total energy of graph. Unlike global energy measures, they provide vertex-level information and allow the identification of structurally significant vertices. In this article, we extend the notion of energy of a vertex \( (\mathcal{E}_{\mathrm G}(v)) \) by defining the general vertex degree-based (VDB) vertex energy. Further, we study some particular types of this invariant, namely the first Zagreb vertex energy \( (\mathcal{M}_1 \mathcal{E}_{\mathrm G}(v)) \), second Zagreb vertex energy \( (\mathcal{M}_2 \mathcal{E}_{\mathrm G}(v)) \), forgotten vertex energy \( (\mathcal{FE}_{\mathrm G}(v)) \), Sombor vertex energy \( (\mathcal{SOE}_{\mathrm G}(v)) \) and atom-bond connectivity vertex energy \( (\mathcal{ABCE}_{\mathrm G}(v)) \), derived from the corresponding VDB topological indices and their associated VDB index-weighted adjacency matrices. Furthermore, using the method proposed by Arizmendi et al., we compute these invariants for certain standard graphs. Subsequently, we perform a vertex-level regression analysis between the eigenvector centrality measure \( (\mathcal{X}_i) \) and these particular VDB vertex energy invariants, with reference to each of the 18 octane isomers, through which we observe a strong correlation between these parameters, thereby establishing their significance.