Discrete curvature on graphs from the effective resistance by Devriendt, K, Lambiotte, R

“…We propose a curvature on the nodes and links of a graph and present the evidence for their interpretation as a curvature. …”

Augmentations of Forman's Ricci curvature and their applications in community detection by Fesser, L, Serrano de Haro Iváñez, S, Devriendt, K, Weber, M, Lambiotte, R

“…The notion of curvature on graphs has recently gained traction in the networks com- munity, with the Ollivier-Ricci curvature (ORC) in particular being used for several tasks in network analysis, such as community detection. …”

Unified synthetic Ricci curvature lower bounds for Riemannian and sub-Riemannian structures by Barilari, D, Mondino, A, Rizzi, L

“…Recent advances in the theory of metric measures spaces on the one hand, and of sub-Riemannian ones on the other hand, suggest the possibility of a "great unification" of Riemannian and sub-Riemannian geometries in a comprehensive framework of synthetic Ricci curvature lower bounds. With the aim of achieving such a unification program, in this paper we initiate the study of gauge metric measure spaces.…”

Burer-Monteiro ADMM for large-scale SDPs by Chen, Y, Goulart, P

“…We prove that our ADMM algorithm converges globally to a first-order stationary point, and show by exploiting the negative curvature that the algorithm converges to a point within O(1−1/r) of the optimal objective value. …”