Financial markets, being spectacular examples of complex systems, display rich correlation structures among price returns of different assets. The correlation structures change drastically, akin to critical phenomena in physics, as do the influential stocks (leaders) and sectors (communities), during market events like crashes. It is crucial to detect their signatures for timely intervention or prevention. Here we use eigenvalue decomposition and eigen-entropy, computed from eigenvector centralities of different stocks in the cross-correlation matrix, to extract information about the disorder in the market. We construct a ‘phase space’, where different market events (bubbles, crashes, etc) undergo phase separation and display order–disorder movements. An entropy functional exhibits scaling behavior. We propose a generic indicator that facilitates the continuous monitoring of the internal structure of the market—important for managing risk and stress-testing the financial system. Our methodology would help in understanding and foreseeing tipping points or fluctuation patterns in complex systems.

金融市场是复杂系统的典范，在不同资产的价格收益之间显示出丰富的相关结构。在市场崩溃之类的市场事件期间，相关结构急剧变化，类似于物理学中的关键现象，而有影响力的股票（领导者）和行业（社区）也是如此。检测他们的签名以进行及时干预或预防至关重要。在这里，我们使用根据互相关矩阵中不同股票的特征向量中心性计算出的特征值分解和特征熵来提取有关市场无序的信息。我们构建了一个“阶段空间”，其中不同的市场事件（泡沫，崩溃等）经历了阶段分离和展示秩序–无序运动。熵函数表现出缩放行为。我们提出了一个通用指标，该指标有助于对市场内部结构进行连续监控，这对于管理风险和对金融系统进行压力测试很重要。我们的方法将有助于理解和预测复杂系统中的临界点或波动模式。