https://neckpinch.com/authors/liang-zhao/New arXiv papers by Liang Zhao, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2606.26750/arxiv:2606.26750Thu, 25 Jun 2026 00:00:00 GMTJuan Zhao, Jicheng Ma, Yunyan Yang, Liang Zhao — In this paper, we first propose two different quantities on graphs, namely local entropy and cohesion, then design two corresponding flows for edge weights: the local entropy flow and the cohesion flow. We establish the global existence and uniqueness of solutions for both flows and investigate their asymptotic behaviors, including the case that the limit goes to positive infinity. Moreover, they can be applied to fundamental network analysis tasks, including community detection and node classification. Empirical evaluations demonstrate that our method achieves performance competitive with Ollivier Ricci flow and Lin-Lu-Yau Ricci flow on benchmark network analysis tasks. In experimental scenarios, we first apply the cohesion flow to evolve the edge weights of the graph, and then apply the local entropy flow to further update the resulting weighted graph. Both flows are computationally efficient, leading to a significant reduction in overall computational cost and improved scalability.Ricci flowKähler geometryStability & uniquenessLong-time existence & convergenceDiscrete & graph Ricci https://neckpinch.com/papers/2508.01400/arxiv:2508.01400Sat, 02 Aug 2025 00:00:00 GMTJuan Zhao, Jicheng Ma, Yunyan Yang, Liang Zhao — 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.Ricci flowDiscrete & graph Ricci