Ollivier-Ricci Curvature Knowledge Graphs Comorbidity Application
Psychiatric disorders share genetic liability, clinical comorbidity, and proposed biological mechanisms. Network models represent this overlap by placing disorders at nodes and mechanism relationships at edges — but standard structural analysis conflates structurally interesting connectivity with the trivial consequences of having many edges. We apply edge-level discrete curvature to separate genuine structural anomalies from degree artifacts.
Curvature in Psychiatric Mechanism Networks
Edge-Level Discrete Curvature Identifies Structurally Anomalous Connections in a Psychiatric Mechanism Network
Application
A 130-node, 218-edge knowledge graph from an expert-adjudicated catalog of 84 psychiatric mechanistic claims linked through 19 shared biological mechanisms. Ollivier-Ricci curvature applied to edges, combined with a degree-preserving permutation null, shows that node-level curvature remains a degree artifact (r = -0.71, p < 0.001), while edge-level curvature resolves genuine structure. Four edges carry more negative curvature than degree predicts, all involving depression or bipolar disorder bridging cross-domain mechanisms: the depression-convergence hub (z = -5.46), depression-metabolic (z = -3.93), bipolar-metabolic (z = -3.33), and depression-circadian (z = -2.62). Disconfirmed claims occupy significantly lower-curvature positions than all other verdict tiers (Cohen’s d = 0.89, n = 84). On seven independent graphs spanning five data types and three disease domains, within-cluster edges have higher curvature than cross-cluster edges in all seven (4/6 significant, d = 0.46-1.55).