Related papers: An Efficient Entropy Flow on Weighted Graphs: Theo…

We study the existence of solutions of Ricci flow equations of Ollivier-Lin-Lu-Yau curvature defined on weighted graphs. Our work is motivated by\cite{NLLG} in which the discrete time Ricci flow algorithm has been applied successfully as a…

In this paper, we propose a modified Ricci flow, as well as a quasi-normalized Ricci flow, on arbitrary weighted graph. Each of these two flows has a unique global solution. In particular, these global existence and uniqueness results do…

Community detection is an important problem in graph neural networks. Recently, algorithms based on Ricci curvature flows have gained significant attention. It was suggested by Ollivier (2009), and applied to community detection by Ni et al…

Ricci curvature and Ricci flow have proven to be powerful tools for analyzing the geometry of discrete structures, particularly on undirected graphs, where they have been applied to tasks ranging from community detection to graph…

Many complex networks in the real world have community structures -- groups of well-connected nodes with important functional roles. It has been well recognized that the identification of communities bears numerous practical applications.…

Community detection in complex networks is a fundamental problem, open to new approaches in various scientific settings. We introduce a novel community detection method, based on Ricci flow on graphs. Our technique iteratively updates edge…

We present a notion of super Ricci flow for time-dependent finite weighted graphs. A challenging feature is that these flows typically encounter singularities where the underlying graph structure changes. Our notion is robust enough to…

Graph Ricci curvature is crucial as it geometrically quantifies network structure. It pinpoints bottlenecks via negative curvature, identifies cohesive communities with positive curvature, and highlights robust hubs. This guides network…

In this paper, we introduce a novel method for extending Ricci flow to hypergraphs by defining probability measures on the edges and transporting them on the line expansion. This approach yields a new weighting on the edges, which proves…

Graph embedding approaches attempt to project graphs into geometric entities, i.e, manifolds. The idea is that the geometric properties of the projected manifolds are helpful in the inference of graph properties. However, if the choice of…

Community detection in hypergraphs is both instrumental for functional module identification and intricate due to higher-order interactions among nodes. We define a hypergraph Ricci flow that directly operates on higher-order interactions…

On a connected finite graph, we propose an evolution of weights including Ollivier's Ricci flow as a special case. During the evolution process, on each edge, the speed of change of weight is exactly the difference between the Wasserstein…

Following [21, 23], the present work investigates a new relative entropy-regularized algorithm for solving the optimal transport on a graph problem within the randomized shortest paths formalism. More precisely, a unit flow is injected into…

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…

Community detection remains an important problem in data mining, owing to the lack of scalable algorithms that exploit all aspects of available data - namely the directionality of flow of information and the dynamics thereof. Most existing…

Ricci curvature and its associated flow offer powerful geometric methods for analyzing complex networks. While existing research heavily focuses on applications for undirected graphs such as community detection and core extraction, there…

This report presents a very simple algorithm for overlaping community-detection in large graphs under constraints such as the minimum and maximum number of members allowed. The algorithm is based on the simulation of random walks and…

Community detection of network flows conventionally assumes one-step dynamics on the links. For sparse networks and interest in large-scale structures, longer timescales may be more appropriate. Oppositely, for large networks and interest…

Unsupervised node clustering (or community detection) is a classical graph learning task. In this paper, we study algorithms, which exploit the geometry of the graph to identify densely connected substructures, which form clusters or…

The computation of electrical flows is a crucial primitive for many recently proposed optimization algorithms on weighted networks. While typically implemented as a centralized subroutine, the ability to perform this task in a fully…