SIAM Journal on Applied Mathematics, Volume 80, Issue 3, Page 1392-1419, January 2020.
Maximizing the modularity of a network is a successful tool to identify an important community of nodes. However, this combinatorial optimization problem is known to be NP-complete. Inspired by recent nonlinear modularity eigenvector approaches, we introduce the modularity total variation $TV_Q$ and show that its box-constrained global maximum coincides with the maximum of the original discrete modularity function. Thus we describe a new nonlinear optimization approach to solve the equivalent problem leading to a community detection strategy based on $TV_Q$. The proposed approach relies on the use of a fast first-order method that embeds a tailored active-set strategy. We report extensive numerical comparisons with standard matrix-based approaches and the Generalized RatioDCA approach for nonlinear modularity eigenvectors, showing that our new method compares favorably with state-of-the-art alternatives.

中文翻译：

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使用非线性优化方法的基于总变异的社区检测

SIAM应用数学杂志，第80卷，第3期，第1392-1419页，2020年1月。
最大化网络的模块化是识别重要节点社区的成功工具。但是，已知此组合优化问题是NP完全的。受最近非线性模块化特征向量方法的启发，我们引入了模块化总变化量$ TV_Q $，并表明其盒约束全局最大值与原始离散模块化函数的最大值一致。因此，我们描述了一种新的非线性优化方法来解决等效问题，从而导致基于$ TV_Q $的社区检测策略。提出的方法依赖于嵌入嵌入量身定制的主动集策略的快速一阶方法的使用。我们报告了基于非线性矩阵特征向量的基于标准矩阵的方法和广义RatioDCA方法的大量数值比较，