标题： 在统计验证的股票网络中寻找核心平衡模块 显示英文标题

标题： Finding Core Balanced Modules in Statistically Validated Stock Networks

摘要： 基于传统阈值的股票网络存在主观参数选择和固有局限性：它们将关系限制为二进制表示，无法捕捉相关强度和负依赖关系。 为解决这一问题，我们引入了经过统计验证的相关性网络，通过皮尔逊系数的严格t检验仅保留具有统计显著性的相关性。 随后，我们提出了一种新的结构，称为最大强相关平衡模块（LSCBM），其定义为具有结构平衡（即所有三元组的正边积）且具有强成对相关性的最大规模股票组。 这种平衡条件确保了稳定的关系，从而通过负边促进潜在的对冲机会。 理论上，在随机带符号图模型中，我们建立了LSCBM在不同参数条件下渐近存在性、大小缩放和多重性。 为了高效检测LSCBM，我们开发了MaxBalanceCore算法，该算法利用了网络稀疏性。 模拟验证了其效率，展示了在数十秒内扩展到最多10,000个节点的网络的能力。 实证分析表明，LSCBM能够识别出对经济变化和危机做出动态重组的核心市场子系统。 在中国股票市场（2013-2024年），在高压力时期（如2015年崩盘）LSCBM的规模激增，在稳定或碎片化阶段则收缩，而其组成每年在主导行业（如工业和金融）之间轮换。 显示英文摘要

摘要： Traditional threshold-based stock networks suffer from subjective parameter selection and inherent limitations: they constrain relationships to binary representations, failing to capture both correlation strength and negative dependencies. To address this, we introduce statistically validated correlation networks that retain only statistically significant correlations via a rigorous t-test of Pearson coefficients. We then propose a novel structure termed the largest strong-correlation balanced module (LSCBM), defined as the maximum-size group of stocks with structural balance (i.e., positive edge-ign products for all triplets) and strong pairwise correlations. This balance condition ensures stable relationships, thus facilitating potential hedging opportunities through negative edges. Theoretically, within a random signed graph model, we establish LSCBM's asymptotic existence, size scaling, and multiplicity under various parameter regimes. To detect LSCBM efficiently, we develop MaxBalanceCore, a heuristic algorithm that leverages network sparsity. Simulations validate its efficiency, demonstrating scalability to networks of up to 10,000 nodes within tens of seconds. Empirical analysis demonstrates that LSCBM identifies core market subsystems that dynamically reorganize in response to economic shifts and crises. In the Chinese stock market (2013-2024), LSCBM's size surges during high-stress periods (e.g., the 2015 crash) and contracts during stable or fragmented regimes, while its composition rotates annually across dominant sectors (e.g., Industrials and Financials).