https://neckpinch.com/authors/jicheng-ma/New arXiv papers by Jicheng Ma, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2606.26750arxiv: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://arxiv.org/abs/2508.01400arxiv: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 https://arxiv.org/abs/2411.06393arxiv:2411.06393Sun, 10 Nov 2024 00:00:00 GMTJicheng Ma, Yunyan Yang — 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 distance related to two probability measures and certain graph distance. Here the probability measure may be chosen as an α-lazy one-step random walk, an α-lazy two-step random walk, or a general probability measure. Based on the ODE theory, we show that the initial value problem has a unique global solution. A discrete version of the above evolution is applied to the problem of community detection. Our algorithm is based on such a discrete evolution, where probability measures are chosen as α-lazy one-step random walk and α-lazy two-step random walk respectively. Note that the latter measure has not been used in previous works. Moreover, only one surgery needs to be performed after the last iteration, which makes our algorithm much simpler than earlier ones based on Lin-Lu-Yau's Ricci curvature.Ricci flowSurgeryLong-time existence & convergenceDiscrete & graph Ricci https://arxiv.org/abs/2408.09435arxiv:2408.09435Sun, 18 Aug 2024 00:00:00 GMTJicheng Ma, Yunyan Yang — 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 not require an exit condition proposed by Bai et al in a recent work [2]. As applications, these two Ricci flows are applied to community detection for complex networks, including Karate Club, American football games, Facebook, as well as artificial networks. In our algorithms, unlike in [5,15], there is no need to perform surgery at every iteration, only one surgery needs to be performed after the last iteration. From three commonly used criteria for evaluating community detection algorithms, ARI, NMI and Q, we conclude that our algorithms outperform existing algorithms, including Ollivier's Ricci flow [5], normalized Ollivier's Ricci flow and normalized Lin-Lu-Yau's Ricci flow [15]. The codes for our algorithms are available at https://github.com/mjc191812/Modified-Ricci-Flow.Ricci flowSurgeryStability & uniquenessLong-time existence & convergenceDiscrete & graph Ricci