Based on the cryptocurrency market dynamics, this study presents a general methodology for analyzing evolving correlation structures in complex systems using the $q$-dependent detrended cross-correlation coefficient \rho(q,s). By extending traditional metrics, this approach captures correlations at varying fluctuation amplitudes and time scales. The method employs $q$-dependent minimum spanning trees ($q$MSTs) to visualize evolving network structures. Using minute-by-minute exchange rate data for 140 cryptocurrencies on Binance (Jan 2021-Oct 2024), a rolling window analysis reveals significant shifts in $q$MSTs, notably around April 2022 during the Terra/Luna crash. Initially centralized around Bitcoin (BTC), the network later decentralized, with Ethereum (ETH) and others gaining prominence. Spectral analysis confirms BTC's declining dominance and increased diversification among assets. A key finding is that medium-scale fluctuations exhibit stronger correlations than large-scale ones, with $q$MSTs based on the latter being more decentralized. Properly exploiting such facts may offer the possibility of a more flexible optimal portfolio construction. Distance metrics highlight that major disruptions amplify correlation differences, leading to fully decentralized structures during crashes. These results demonstrate $q$MSTs' effectiveness in uncovering fluctuation-dependent correlations, with potential applications beyond finance, including biology, social and other complex systems.

翻译：基于加密货币市场的动力学特性，本研究提出了一种通用方法，利用$q$依赖的去趋势互相关系数$\\rho(q,s)$来分析复杂系统中演化的关联结构。通过扩展传统度量指标，该方法能够捕捉不同波动幅度和时间尺度下的相关性。该方法采用$q$依赖的最小生成树（$q$MSTs）来可视化演化的网络结构。使用币安（Binance）上140种加密货币的每分钟汇率数据（2021年1月至2024年10月），滚动窗口分析揭示了$q$MSTs的显著变化，特别是在2022年4月Terra/Luna崩盘期间。网络最初以比特币（BTC）为中心，随后逐渐去中心化，以太坊（ETH）及其他资产的重要性提升。谱分析证实了BTC主导地位的下降以及资产间多样性的增加。一个关键发现是，中等规模波动表现出比大规模波动更强的相关性，而基于后者的$q$MSTs更为去中心化。充分利用这些事实可能为构建更灵活的最优投资组合提供可能。距离度量指标突显了重大市场冲击会放大关联差异，导致崩盘期间出现完全去中心化的结构。这些结果证明了$q$MSTs在揭示依赖波动的相关性方面的有效性，其潜在应用可扩展至金融以外的领域，包括生物学、社会学及其他复杂系统。