In this study, two basic labeling techniques, namely vertex and edge labeling techniques are investigated for their use in computational biology particularly in the solution of protein-protein interaction (PPI) networks, gene regulatory networks (GRNs), and metabolic pathway analysis. By implementing graph-based methods, we identified key proteins with high centrality measures, such as P53 (degree centrality: Among them, TP53 (eigenvalue: 0. 148) and AKT1 (betweenness centrality: 0. 089) are particularly imperative in cellular process. Community detection revealed functional modules linked to cell cycle regulation and cancer signaling, while pathway enrichment analysis in GRNs highlighted critical processes such as apoptosis (p-value: which goes up to 0. 001 for emotional state and to 0. 005 for immune response. Morphological analysis of metabolic networks revealed some of the constraints such as decrease in ATP yield because of the low activity of pyruvate kinase. These results stress the value of the models based on vertex and edge labeling for the understanding of the organization of the biological networks and their components in the context of protein-protein interactions, gene expression regulation and metabolic pathways. Combination of these methods improves knowledge about biological systems and yields useful information in some therapeutic and disease-related investigations.