We adapt Forman's discretization of Ricci curvature to the case of undirected networks, both
weighted and unweighted, and investigate the measure in a variety of model and real-world …

This article introduces a new approach to discrete curvature based on the concept of
effective resistances. We propose a curvature on the nodes and links of a graph and present …

The complexity of financial markets arise from the strategic interactions among agents
trading stocks, which manifest in the form of vibrant correlation patterns among stock prices …

Geometric deep learning has demonstrated a great potential in non-Euclidean data
analysis. The incorporation of geometric insights into learning architecture is vital to its …

Connections between continuous and discrete worlds tend to be elusive. One example is
curvature. Even though there exist numerous nonequivalent definitions of graph curvature …

We consider a formal discretisation of Euclidean quantum gravity defined by a statistical
model of random 3-regular graphs and making using of the Ollivier curvature, a coarse …

Introduction Geometry-inspired notions of discrete Ricci curvature have been successfully
used as markers of disrupted brain connectivity in neuropsychiatric disorders, but their ability …

Community structure is a fundamental topological characteristic of optimally organized brain
networks. Currently, there is no clear standard or systematic approach for selecting the most …