Discrete Ricci Curvature on Complex Network Topologies: An Application to Management Information System Networks

Discrete Ricci curvature has been applied to biological, financial, and communication graphs, but typed management information system (MIS) transaction networks still lack MIS-specific analytical guarantees and a reproducible, operationally interpretable workflow. We combine Ollivier–Ricci optimal transport with a role-based access control representation of users, roles, services, endpoints, and databases. Closed-form results show that edges joining a hub to degree-one leaves have non-negative curvature, whereas canonical inter-hub bridges converge to curvature −1 when the idleness parameter is α=0.5. We also prove the existence of an optimal coupling on finite graphs and explain why the coupling itself need not be unique. On a reproducible synthetic MIS network, the curvature ranks authentication, shared-data, and cross-module links among the leading candidate bottlenecks and correlates with edge betweenness (Spearman ρ=−0.78). Across 40 randomized MIS instances, graph-instance-level edge-class differences are significant (Friedman p<10−32), and all five leading edges belong to predefined structural bridge classes in every run. On five public Internet backbones, curvature–betweenness correlations range from −0.53 to −0.91. Comparisons with Forman curvature, local edge connectivity, algebraic connectivity loss, and a spectral embedding show a complementary geometric signal rather than a universal cut-edge or spectral surrogate. We additionally report the idleness parameter sensitivity, empirical runtime and process memory measurements, study limitations, and a conceptual temporal extension.