Abstract：The substructure of stock network, e.g. community, is investigated based on the synchronization theory by utilizing the correlation matrix of time series of stock price fluctuation. Through the spectral analysis on the correlation matrix, it’s determined that the complicated community structure obviously exists in the stock network. Then, the clustering algorithm based on the synchronization theory incorporating with the Kuramoto model is used to dynamically identify the community structure, which suggests that the groups of stocks well agree with the taxonomy of stock market. We also apply the fast community detecting algorithm to verify the former results with respect to the same parametric constrains.
麻景豪, 蔡世民. 基于同步理论的股票网络社团识别研究[J]. 复杂系统与复杂性科学, 2014, 11(4): 48-53.
MA Jinghao, CAI Shimin. Study on Community Identification of Stock Network Based on Synchronization Theory[J]. Complex Systems and Complexity Science, 2014, 11(4): 48-53.
[1] Winfree A T. The Geometry of Biological Time[M]. New York:Springer, 2001. [2] Strogatz S H. Sync:the Emerging Science of Spontaneous Order[M]. New York:Hyperion, 2003. [3] Arenas A, Díaz-Guilera A, Kurths J, et al. Synchronization in complex networks[J]. Phys Rep, 2008, 469（3):93-153. [4] Kuramoto Y. Chemical Oscillations, Waves, and Turbulence[M]. New York:Courier Dover Publications, 2003. [5] Arenas A, Díaz-Guilera A, Pérez-Vicente C J. Synchronization reveals topological scales in complex networks[J]. Phys Rev Lett, 2006, 96（11):114102. [6] Mantegna R N. Hierarchical structure in financial markets[J]. Eur J Phys B, 1999, 11（1):193-197. [7] Bonanno G, Caldarelli G, Lillo F, et al. Topology of correlation-based minimal spanning trees in real and model markets[J]. Phys Rev E, 2003, 68（4):046130. [8] Onnela J P, Chakraborti A, Kaski K, et al. Dynamics of market correlations:taxonomy and portfolio analysis[J]. Phys Rev E, 2003, 68（5):056110. [9] Cai S M, Zhou Y B, Zhou T, et al. Hierarchical organization and disassortative mixing of correlation-based weighted financial networks[J]. Int J Mod Phys C, 2010, 21（3):135005. [10] 蔡世民, 洪磊, 傅忠谦, 等. 基于复杂网络的金融市场网络结构实证研究[J]. 复杂系统与复杂性科学, 2011, 8（3):29-33. Cai Shimin, Hong Lei, Fu Zhongqian, et al. Empirical study on network structure of financial market based on complex network theory[J]. Complex System and Complexity Science, 2011, 8（3):29-33. [11] Gao Y C, Wei Z W, Wang B H, Dynamic evolution of financial network and its relation to economic cries[J]. Int J Mod Phys C, 2013, 24（2):433-441. [12] Plerou V, Gopikrishnan P, Rosenow B, et al. Universal and nonuniversal properties of cross correlations in financial time series[J]. Phys Rev Lett, 1999, 83（7):1471. [13] Plerou V, Gopikrishnan P, Rosenow B, et al. Random matrix approach to cross correlations in financial data[J]. Phys Rev E, 2002, 65（6):066126. [14] Gopikrishnan P, Rosenow B, Plerou V, et al. Quantifying and interpreting collective behavior in financial markets[J]. Phys Rev E, 2001, 64（3):035106. [15] Kim D H, Jeong H. Systematic analysis of group identification in stock markets[J]. Phys Rev E, 2005, 72（4):046133. [16] Lee D S. Synchronization transition in scale-free networks:clusters of synchrony[J]. Phys Rev E, 2005, 72（2):026208. [17] Donetti L, Hurtado P I, Munoz M A. Entangled networks, synchronization, and optimal network topology[J]. Phys Rev Lett, 2005, 95（18):188701. [18] Chavez M, Hwang D U, Amann A, et al. Synchronization is enhanced in weighted complex networks[J]. Phys Rev Lett, 2005, 94（21):218701. [19] Miyano T, Tsutsui T. Data synchronization in a network of coupled phase oscillators[J]. Phys Rev Lett, 2007, 98（2):024102. [20] Shao J, Plant C, Yang Q, et al. Detection of arbitrarily oriented synchronized clusters in high-dimensional data[C]//Proceedings of 11th IEEE International Conference on Data Mining. 2011:607-616. [21] Hong L, Cai S M, Zhang J, et al. Synchronization-based approach for detecting functional activation of brain[J]. Chaos, 2012, 22（3):033128. [22] Newman M E J. Fast algorithm for detecting community structure in networks[J]. Phys Rev E, 2004, 69（6):066133. [23] Zhuo Z, Cai S M, Fu Z Q, et al. Hierarchical organization of brain functional networks during visual tasks[J]. Phys Rev E, 2011, 84（3):031923.
