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

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…

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…

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…

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…

Many biological and social systems are naturally represented as edge-weighted directed or undirected hypergraphs since they exhibit group interactions involving three or more system units as opposed to pairwise interactions that can be…

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…

Motivated by the methods and results of manifold sampling based on Ricci curvature, we propose a similar approach for networks. To this end we make appeal to three types of discrete curvature, namely the graph Forman-, full Forman- and…

A novel method to identify salient computational paths within randomly wired neural networks before training is proposed. The computational graph is pruned based on a node mass probability function defined by local graph measures and…

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…

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…

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 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…

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…

We propose a novel entropy flow on weighted graphs, which provides a principled framework that characterizes the evolution of probability distributions over graph structures while sharing geometric intuition with discrete Ricci flow. We…

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…

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…

Characterizing shapes of high-dimensional objects via Ricci curvatures plays a critical role in many research areas in mathematics and physics. However, even though several discretizations of Ricci curvatures for discrete combinatorial…

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…

In this paper, we consider the problem of approximately aligning/matching two graphs. Given two graphs $G_{1}=(V_{1},E_{1})$ and $G_{2}=(V_{2},E_{2})$, the objective is to map nodes $u, v \in G_1$ to nodes $u',v'\in G_2$ such that when $u,…