Structural control and resilience in the oxytocin molecular graph: A graph-theoretic framework for critical atom and...

Graph-theoretic analysis provides a rigorous mathematical framework for investigating molecular architecture; however most existing studies primarily rely on conventional topological indices and centrality measures that characterize connectivity without explicitly quantifying structural control, redundancy, vulnerability or resilience. This study develops a unified graph-theoretic framework for resilience-oriented analysis of cyclic peptide molecular graphs through a collection of novel connectivity-based descriptors. Oxytocin is selected as the principal case study because of its well-defined cyclic architecture and conserved disulfide bridge, four additional cyclic peptides: Vasopressin, Desmopressin, Octreotide and Somatostatin are analyzed to validate the robustness, discriminative capability and general applicability of the proposed methodology. Hydrogen-suppressed molecular graphs were constructed from experimentally established molecular structures. In addition to classical graph-theoretic measures including degree, betweenness, closeness, eigenvector centralities and network efficiency, the proposed framework introduces the Enhanced Structural Control Index (ESCI), Bond Criticality Index (BCI), Weighted Bond Criticality Index (WBCI), Disulfide Structural Redundancy Index (DSRI), Atom Vulnerability Spectrum (AVS) and Molecular Resilience Ratio (MRR). Structural robustness was further investigated by comparing targeted perturbations performed through sequential removal of the five highest-ranked AVS atoms with random vertex deletions. The oxytocin molecular graph contains 69 vertices, 71 edges and a cyclomatic number of three revealing strong dependence on a limited set of articulation points and bridge edges. AVS exhibits a strong correlation with betweenness centrality (Pearson correlation >0.91 across all investigated peptides) while providing complementary efficiency-based vulnerability information beyond conventional centrality measures. Comparative validation across five cyclic peptide molecular graphs demonstrates that the proposed descriptors consistently distinguish structural control, bond criticality, redundancy, vulnerability and resilience. The proposed framework establishes a mathematically interpretable, computationally efficient and broadly applicable methodology for graph-theoretic analysis of cyclic peptide molecular graphs with potential extensions to larger peptide systems and related biomolecular networks.