标题： 通过加权图上的里奇曲率流进行核心检测 显示英文标题

标题： Core detection via Ricci curvature flows on weighted graphs

摘要： 图Ricci曲率至关重要，因为它几何地量化了网络结构。 它通过负曲率确定瓶颈，通过正曲率识别紧密社区，并突出显示强大的中心节点。 这指导了网络分析、弹性评估、流优化和有效算法设计。 在本文中，我们推导了多种离散Ricci曲率流中权重的上下界。 作为应用，我们利用离散Ricci曲率流来检测有限无向图的核心子图。 这项工作的创新之处有两个方面。 首先，在Ricci曲率流过程中，权重的边界决定了确保权重保持在两个预定正常数之间的最小迭代次数。 特别是，对于任何固定图，我们得出结论，只要迭代次数不超过一定数量，权重既不会溢出也不会被视为零；其次，它表明我们的Ricci曲率流方法在识别核心子图方面优于先前的方法，如PageRank、度中心性、介数中心性和接近中心性。 我们算法的代码可在 https://github.com/12tangze12/core-detection-via-Ricci-flow 获取。 显示英文摘要

摘要： 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 analysis, resilience assessment, flow optimization, and effective algorithm design. In this paper, we derived upper and lower bounds for the weights along several kinds of discrete Ricci curvature flows. As an application, we utilized discrete Ricci curvature flows to detect the core subgraph of a finite undirected graph. The novelty of this work has two aspects. Firstly, along the Ricci curvature flow, the bounds for weights determine the minimum number of iterations required to ensure weights remain between two prescribed positive constants. In particular, for any fixed graph, we conclude weights can not overflow and can not be treated as zero, as long as the iteration does not exceed a certain number of times; Secondly, it demonstrates that our Ricci curvature flow method for identifying core subgraphs outperforms prior approaches, such as page rank, degree centrality, betweenness centrality and closeness centrality. The codes for our algorithms are available at https://github.com/12tangze12/core-detection-via-Ricci-flow.