Related papers: A modified Ricci flow on arbitrary weighted graph

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…

Many community detection algorithms have been developed to uncover the mesoscopic properties of complex networks. However how good an algorithm is, in terms of accuracy and computing time, remains still open. Testing algorithms on…

In cerebrovascular networks, some vertices are more connected to each other than with the rest of the vasculature, defining a community structure. Here, we introduce a class of model networks built by rewiring Random Regular Graphs, which…

There are fundamental differences between citation networks and other classes of graphs. In particular, given that citation networks are directed and acyclic, methods developed primarily for use with undirected social network data may face…

We give the global picture of the normalized Ricci flow on generalized flag manifolds with two or three isotropy summands. The normalized Ricci flow for these spaces descents to a parameter depending system of two or three ordinary…

In this paper, we study the Bakry-\'Emery Ricci flow on finite graphs. Our main result is the local existence and uniqueness of solutions to the Ricci flow. We prove the long-time convergence or finite-time blow up for the Bakry-\'Emery…

In this paper, we investigate the behavior of the normalized Ricci flow on asymptotically hyperbolic manifolds. We show that the normalized Ricci flow exists globally and converges to an Einstein metric when starting from a non-degenerate…

We develop a stochastic target representation for Ricci flow and normalized Ricci flow on smooth, compact surfaces, analogous to Soner and Touzi's representation of mean curvature flow. We prove a verification/uniqueness theorem, and then…

It is often of interest to find communities in network data for unsupervised learning, feature discovery, anomaly detection, or scientific study. The vast majority of community detection methods proceed via optimization of a quality…

Graph algorithms applied in many applications, including social networks, communication networks, VLSI design, graphics, and several others, require dynamic modifications -- addition and removal of vertices and/or edges -- in the graph.…

In this work, we propose to utilize discrete graph Ricci flow to alter network entropy through feedback control. Given such feedback input can reverse entropic changes, we adapt the moniker of Maxwells Demon to motivate our approach. In…

In this paper we give an explicit bound of $\Delta_{g(t)}u(t)$ and the local curvature estimates for the Ricci-harmonic flow under the condition that the Ricci curvature is bounded along the flow. In the second part these local curvature…

The investigation of community structures in networks is an important issue in many domains and disciplines. This problem is relevant for social tasks (objective analysis of relationships on the web), biological inquiries (functional…

We develop a perturbative formulation of the Ricci flow in gravity. Following steps analogous to the gradient flow in QCD, we supplement the usual Feynman rules for perturbative gravity by flowed propagators and vertices as well as graviton…

In this paper we investigate a kind of generalized Ricci flow which possesses a gradient form. We study the monotonicity of the given function under the generalized Ricci flow and prove that the related system of partial differential…

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…

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…

Community detection in social networks is a problem with considerable interest, since, discovering communities reveals hidden information about networks. There exist many algorithms to detect inherent community structures and recently few…

Educational data mining has become an important research field in studying the social behavior of college students using massive data. However, traditional campus friendship network and their community detection algorithms, which lack time…

Traditional manifold learning algorithms often bear an assumption that the local neighborhood of any point on embedded manifold is roughly equal to the tangent space at that point without considering the curvature. The curvature indifferent…