Community detection by the normalized Ricci flow with the optimization of the information entropy

Discrete Ricci curvature serves as a fundamental geometric tool for quantifying the structural characteristics of complex networks, effectively capturing the richness of their connection patterns. Building on this theoretical framework, this paper proposes an improved discrete Ricci curvature algorithm enhanced by information entropy optimization. Through a systematic analysis of the correlation between curvature and node degree in representative network models, we study the intrinsic relationship between Ricci curvature and community structure. Experimental results on multiple real-world networks and the Lancichinetti-Fortunato-Radicchi benchmark model demonstrate that the proposed algorithm adaptively optimizes key parameters, leading to significant improvements in both the accuracy and robustness of community detection. Moreover, it consistently outperforms existing methods across various network scales and mixing parameters.