Ollivier Ricci Curvature

Ollivier-Ricci curvature (ORC) is a geometric measure applied to networks and graphs, quantifying the curvature of a space based on the Wasserstein distance between probability distributions of random walks. Current research focuses on efficient computation of ORC, particularly for large-scale networks and hypergraphs, and its application in diverse fields such as manifold learning, healthcare network analysis, and graph neural network optimization. ORC's ability to reveal structural properties of complex networks offers valuable insights for improving algorithms and understanding the underlying geometry of data, impacting fields ranging from data analysis to human behavior modeling.