相关论文: Core detection via Ricci curvature flows on weight…

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…

Ricci curvature was proposed by Ollivier in a general framework of metric measure spaces, and it has been studied extensively in the context of graphs in recent years. In this paper we prove upper bounds for Ollivier's Ricci curvature for…

We develop a new and systematic method for proving entropic Ricci curvature lower bounds for Markov chains on discrete sets. Using different methods, such bounds have recently been obtained in several examples (e.g., 1-dimensional birth and…

We propose RicciFlowRec, a geometric recommendation framework that performs root cause attribution via Ricci curvature and flow on dynamic financial graphs. By modelling evolving interactions among stocks, macroeconomic indicators, and…

Graph neural networks(GNNs) have been demonstrated to depend on whether the node effective information is sufficiently passing. Discrete curvature (Ricci curvature) is used to study graph connectivity and information propagation efficiency…

We use the discrete Ollivier-Ricci graph curvature with Ricci flow to examine the intrinsic geometry of financial markets through the empirical correlation graph of the NASDAQ 100 index. Our main result is the development of a technique to…

We present the application of topological data analysis (TDA) to study unweighted complex networks via their persistent homology. By endowing appropriate weights that capture the inherent topological characteristics of such a network, we…

Graph Neural Networks are highly effective at learning from relational data, leveraging node and edge features while maintaining the symmetries inherent to graph structures. However, many real-world systems, such as social or biological…

We study curvature-driven edge reweighting for community recovery in the balanced two-block stochastic block model. Given a graph G with initial weights equal to the adjacency matrix, we iteratively update edge weights using Lin-Lu-Yau…

Ricci flow deforms the Riemannian metric proportionally to the curvature, such that the curvature evolves according to a heat diffusion process and eventually becomes constant everywhere. Ricci flow has demonstrated its great potential by…

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…

Community and core-periphery are two widely studied graph structures, with their coexistence observed in real-world graphs (Rombach, Porter, Fowler \& Mucha [SIAM J. App. Math. 2014, SIAM Review 2017]). However, the nature of this…

Graph pattern mining methods can extract informative and useful patterns from large-scale graphs and capture underlying principles through the overwhelmed information. Contrast analysis serves as a keystone in various fields and has…

Deep neural networks learn feature representations via complex geometric transformations of the input data manifold. Despite the models' empirical success across domains, our understanding of neural feature representations is still…

We study a modified notion of Ollivier's coarse Ricci curvature on graphs introduced by Lin, Lu, and Yau in [11]. We establish a rigidity theorem for complete graphs that shows a connected finite simple graph is complete if and only if the…

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 a novel definition of curvature for hypergraphs, a natural generalization of graphs, by introducing a multi-marginal optimal transport problem for a naturally defined random walk on the hypergraph. This curvature, termed…

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…

A goal in network science is the geometrical characterization of complex networks. In this direction, we (arXiv:1603.00386; J. Stat. Mech. (2016) P063206) have recently introduced the Forman's discretization of Ricci curvature to the realm…

The importance of studying properties of networks is manifest in diverse fields ranging from biology, engineering, physics, chemistry, neuroscience, and medicine. The functionality of networks with regard to performance, throughput,…