基于复杂网络的金融市场网络结构实证研究

摘要

The adjacency matrix of financial network is obtained based on the thresholding correlation matrix of time series of stock price fluctuation, and analyzed to characterize network properties via measures of complex networks. The cumulative distribution of degree with a fat-tail is presented to suggest that a small number of hub-like stocks exist,and the relationship between clustering and connectivity of vertices emphasizes hierarchical organization. The measurement of average nearest-neighbor degree running over classes of vertices with degree k shows a descending trend with k, which suggests the disassortative mixing of financial network, Furthermore, the k-core decomposition of financial network shows the size of k-core power-law increases with connectivity of vertices at a small scale while keeps same at a large scale, and the vertices of maximal k-core consist with the hub-like stocks of financial market. These interesting results in complex network aspect may provide some insights to deeply understand the underlying evolutional mechanism of financial market.%基于股票价格波动序列的相关特性,通过阈值化处理得到金融网络的连接矩阵,并用复杂网络的特征参量表征其网络性质.节点累积度分布的胖尾特征表明存在少数中心节点的股票,而聚类系数和最紧邻平均度表征金融网络具有层次结构和异配特性.进一步研究k核结构,发现核数随节点度幂律增长,当节点度较大时核数保持不变,而且最核心的节点对应中心节点.这些结论对于从复杂网络的角度理解金融市场演化机制有重要的启示.