The structure of stock markets as signed networks

Document Type: Research Paper


Electrical Engineering faculty, Arak University of Technology, Arak, Iran


Dynamism and evolution in financial markets and specifically stock markets represents a complex network with many relations between different finance agents and corporations. So there are many researches analyzing different aspects of stock markets in the field of complex networks. However, studying financial markets as signed networks maybe considered as a new perspective in this area. This paper proposes a new methodology for analyzing structure of stock markets as signed networks in the perspective of balance theory.  For this purpose, some stock markets based on some data of Tehran stock market and Nasdaq are modeled as signed networks and some aspects of their structural properties were studied from the point of view of balance theory. The results show the whole pattern of the structure of stock networks approximately fit to a completely balanced structure. It is observed that the distance from structural balance rises abruptly in some unstable duration and so may be proposed as an index for forecasting overall function of stock markets or crisis conditions. The results also imply the existence and role of positive connection between two balanced partitions. The proposed methodology can lead directly to many applications in analyzing, evaluating and forecasting stock markets such as balanced clustering and determining the important companies and relations affecting the overall system function. The applications could be useful for system control and decisions either in micro level such as portfolio investment or macro level and regulating the market.


Main Subjects

Allen, F., Babus, A. (2009). Networks in finance, in Kleindorfer P., Wind J. (Eds.), The network challenge, Wharton School Publishing, pp 367–382.


Altafini, C. (2012). Dynamics of opinion forming in structurally balanced social networks. PloS one, 7(6), e38135.


Arcangelis, A.M., Rotundo, G. (2016). Complex Networks in Finance, in Commendatore P., Matilla-García M., Varela L., Cánovas J. (Eds.),  Cánovas J. Complex Networks and Dynamics: Lecture Notes in Economics and Mathematical Systems, vol 683, Springer.


Battiston, S., Glattfelder, J.B., Garlaschelli, D., Lillo, F. and Caldarelli, G., 2010. The structure of financial networks. In: Estrada E., Fox M., Higham D., Oppo GL. (eds) Network Science Springer, London, (pp. 131-163).


Bekiros, S., Nguyen, D. K., Junior, L. S., & Uddin, G. S. (2017). Information diffusion, cluster formation and entropy-based network dynamics in equity and commodity markets. European Journal of Operational Research, 256(3), 945-961.


Cartwright, D., & Harary, F. (1956). Structural balance: a generalization of Heider's theory. Psychological review, 63(5), 277.


Davis, J. A. (1967). Clustering and structural balance in graphs, Human relations, 20(2), 181-187.


Doreian, P., & Mrvar, A. (2009). Partitioning signed social networks. Social Networks, 31(1), 1-11.


Ehsani, M., & Sepehri, M. M. (2014). Balanced clusters and diffusion process in signed networks, Journal of Industrial and Systems Engineering, 7(1), 104-117.


Esfahanipour A., Zamanzadeh S.E. (2013). Stock Market Filtering Model Based on Minimum Spanning Tree in Financial Networks, Amirkabir International Journal of Science & Research, (Vol. 45), No.1, pp. 67 – 75.


Garas, A., Argyrakis, P., & Havlin, S. (2008). The structural role of weak and strong links in a financial market network, The European Physical Journal B, 63(2), 265-271.


He, X., Du, H., Feldman, M.W. and Li, G., 2019. Information diffusion in signed networks. PloS one, 14(10).


Heider, F. (1946). Attitudes and cognitive organization, Journal of Psychology 21, 107–112.


Iacono, G., & Altafini, C. (2010). Monotonicity, frustration, and ordered response: an analysis of the energy landscape of perturbed large-scale biological networks. BMC systems biology, 4(1), 83.


Korbel, J., Jiang, X. and Zheng, B., 2017. Transfer entropy between communities in complex networks. arXiv preprint arXiv:1706.05543.


Lin, C. C., Lee, C. H., Fuh, C. S., Juan, H. F., & Huang, H. C. (2013). Link clustering reveals structural characteristics and biological contexts in signed molecular networks. PloS one, 8(6), e67089.


Mantegna, R.N. (1999). Hierarchical structure in financial markets, The European Physical Journal B-Condensed Matter and Complex Systems, 11(1), 193-197. 


Onnela, J. P., Kaski, K., & Kertész, J. (2004). Clustering and information in correlation based financial networks, The European Physical Journal B, 38(2), 353-362.


Singh, R., Dasgupta, S., & Sinha, S. (2014). Extreme variability in convergence to structural balance in frustrated dynamical systems, EPL (Europhysics Letters), 105(1), 10003.   


Smith, H. L. (2008). Monotone dynamical systems: an introduction to the theory of competitive and cooperative systems (Vol. 41). American Mathematical Soc.


Sontag ED. (2007). Monotone and near-monotone biochemical networks. Systems and Synthetic Biology, 1:59-87.


Su, Y., Wang, B., Cheng, F., Zhang, L., Zhang, X. and Pan, L., 2017. An algorithm based on positive and negative links for community detection in signed networks. Scientific reports, 7(1), pp.1-12.


Traag, V. A., Van Dooren, P., & De Leenheer, P. (2013). Dynamical models explaining social balance and evolution of cooperation. PloS one, 8(4), e60063.


Tse CK. (2010). A network perspective of the stock market, Journal of Empirical Finance, (Volume 17), Issue 4, September, Pages 659-667.