Related papers: Characterizing Physician Referral Networks with Ri…
The characterization of complex networks with tools originating in geometry, for instance through the statistics of so-called Ricci curvatures, is a well established tool of network science. There exist various types of such Ricci…
The human brain forms functional networks on all spatial scales. Modern fMRI scanners allow to resolve functional brain data in high resolutions, allowing to study large-scale networks that relate to cognitive processes. The analysis of…
Temporal networks -- sequences of time-stamped contacts among nodes -- constitute the finest-grained representation of dynamic interaction data; however, geometric and topological analyses of such networks have remained largely confined to…
Networks and their higher order generalizations, such as hypernetworks or multiplex networks are ever more popular models in the applied sciences. However, methods developed for the study of their structural properties go little beyond the…
We introduce Forman-Ricci curvature and its corresponding flow as characteristics for complex networks attempting to extend the common approach of node-based network analysis by edge-based characteristics. Following a theoretical…
The notion of curvature on graphs has recently gained traction in the networks community, with the Ollivier-Ricci curvature (ORC) in particular being used for several tasks in network analysis, such as community detection. In this work, we…
We present a viable solution to the challenging question of change detection in complex networks inferred from large dynamic data sets. Building on Forman's discretization of the classical notion of Ricci curvature, we introduce a novel…
Graph curvature provides geometric priors for Graph Neural Networks (GNNs), enhancing their ability to model complex graph structures, particularly in terms of structural awareness, robustness, and theoretical interpretability. Among…
Networks with higher-order interactions, prevalent in biological, social, and information systems, are naturally represented as hypergraphs, yet their structural complexity poses fundamental challenges for geometric characterization. While…
In recent years extensions of manifold Ricci curvature to discrete combinatorial objects such as graphs and hypergraphs (popularly called as "network shapes"), have found a plethora of applications in a wide spectrum of research areas…
Discrete Forman-Ricci curvature (FRC) is an efficient tool that characterizes essential geometrical features and associated transitions of real-world networks, extending seamlessly to higher-dimensional computations in simplicial complexes.…
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. Importantly, these two discretizations of the Ricci…
Randomly Wired Neural Networks (RWNNs) serve as a valuable testbed for investigating the impact of network topology in deep learning by capturing how different connectivity patterns impact both learning efficiency and model performance. At…
A goal in network science is the geometrical characterization of complex networks. In this direction, we have recently introduced Forman's discretization of Ricci curvature to the realm of undirected networks. Investigation of this…
Analysis of Internet topologies has shown that the Internet topology has negative curvature, measured by Gromov's "thin triangle condition", which is tightly related to core congestion and route reliability. In this work we analyze the…
In this paper we analyze the US Patient Referral Network (also called the Shared Patient Network) and various subnetworks for the years 2009--2015. In these networks two physicians are linked if a patient encounters both of them within a…
We propose a new graph kernel for graph classification and comparison using Ollivier Ricci curvature. The Ricci curvature of an edge in a graph describes the connectivity in the local neighborhood. An edge in a densely connected…
In the present work, we study the properties of biological networks by applying analogous notions of fundamental concepts in Riemannian geometry and optimal mass transport to discrete networks described by weighted graphs. Specifically, we…
Describing networks geometrically through low-dimensional latent metric spaces has helped design efficient learning algorithms, unveil network symmetries and study dynamical network processes. However, latent space embeddings are limited to…
Efficient molecular featurization is one of the major issues for machine learning models in drug design. Here we propose persistent Ricci curvature (PRC), in particular Ollivier persistent Ricci curvature (OPRC), for the molecular…