Detecting network anomalies using Forman–Ricci curvature and a case study for human brain networks [PDF]
Scientific Reports, 2021 We analyze networks of functional correlations between brain regions to identify changes in their structure caused by Attention Deficit Hyperactivity Disorder (adhd).
Tanima Chatterjee +4 more
doaj +3 more sources
Ollivier-Ricci Curvature-Based Method to Community Detection in Complex Networks [PDF]
Scientific Reports, 2019 Identification of community structures in complex network is of crucial importance for understanding the system’s function, organization, robustness and security.
Jayson Sia +2 more
exaly +3 more sources
Ricci curvature: An economic indicator for market fragility and systemic risk [PDF]
Science Advances, 2016 Researchers introduce the geometric concept of curvature toward the application of uncovering systemic risk and market fragility. Quantifying the systemic risk and fragility of financial systems is of vital importance in analyzing market efficiency ...
Tryphon T Georgiou, Allen R Tannenbaum
exaly +3 more sources
Comparative analysis of two discretizations of Ricci curvature for complex networks [PDF]
Scientific Reports, 2018 We have performed an empirical comparison of two distinct notions of discrete Ricci curvature for graphs or networks, namely, the Forman-Ricci curvature and Ollivier-Ricci curvature.
Areejit Samal, Shiping Liu, Emil Saucan
exaly +4 more sources
Ollivier Ricci curvature of directed hypergraphs. [PDF]
Sci Rep, 2020 Many empirical networks incorporate higher order relations between elements and therefore are naturally modelled as, possibly directed and/or weighted, hypergraphs, rather than merely as graphs.
Eidi M, Jost J.
europepmc +9 more sources
On Ricci Curvature of a Homogeneous Generalized Matsumoto Finsler Space
Mathematics, 2023 The characterization of Finsler spaces with Ricci curvature is an ancient and cumbersome one. In this paper, we have derived an expression of Ricci curvature for the homogeneous generalized Matsumoto change.
Yanlin Li +3 more
doaj +2 more sources
On the existence of isoperimetric regions in manifolds with nonnegative Ricci curvature and Euclidean volume growth. [PDF]
Calc Var Partial Differ Equ, 2022 In this paper we provide new existence results for isoperimetric sets of large volume in Riemannian manifolds with nonnegative Ricci curvature and Euclidean volume growth.
Antonelli G +3 more
europepmc +3 more sources
Unfolding the multiscale structure of networks with dynamical Ollivier-Ricci curvature. [PDF]
Nat Commun, 2021 Describing networks geometrically through low-dimensional latent metric spaces has helped design efficient learning algorithms, unveil network symmetries and study dynamical network processes.
Gosztolai A, Arnaudon A.
europepmc +3 more sources
Ricci Curvature on Polyhedral Surfaces via Optimal Transportation [PDF]
Axioms, 2014 The problem of correctly defining geometric objects, such as the curvature, is a hard one in discrete geometry. In 2009, Ollivier defined a notion of curvature applicable to a wide category of measured metric spaces, in particular to graphs.
Benoît Loisel, Pascal Romon
doaj +7 more sources
Measuring robustness of brain networks in autism spectrum disorder with Ricci curvature. [PDF]
Sci Rep, 2020 Ollivier–Ricci curvature is a method for measuring the robustness of connections in a network. In this work, we use curvature to measure changes in robustness of brain networks in children with autism spectrum disorder (ASD).
Simhal AK +7 more
europepmc +2 more sources