Stock market network’s topological stability: Evidence from planar maximally filtered graph and minimal spanning tree

Abstract

We study the topological stability of stock market network by investigating the topological robustness, namely the ability of the network to resist structural or topological changes. The stock market network is extracted by minimal spanning tree (MST) and planar maximally filtered graph (PMFG). We find that the specific delisting thresholds of the listed companies exist in both MST and PMFG networks. In comparison with MST, PMFG provides more information and is better for the aim of exploring stock market network's robustness. The PMFG before the US sub-prime crisis (i.e., from June 2005 to May 2007) has a stronger robustness against the intentional topological damage than the other two sub-periods (i.e.). We also find that the nonfractal property exists in MSTs of S&P 500, i.e., the highly connected nodes link with each other directly, which indicates that the MSTs are vulnerable to the removal of such important nodes. Moreover, the financial institutions and high technology companies are important in maintaining the stability of S&P 500 network. networks, the minimum spanning tree (MST) and the planar maximally filtered graph (PMFG) are introduced in previous studies. 1,2 The MST method is widely used in different financial market networks. 11,23-26 In a MST, only N − 1 links out of the original N (N − 1)/2 links are kept to connect all the nodes together with a minimal total distance. It should be pointed out that the completely connected network contains more information than the hierarchical MST. To give filtered graphs that contain more information, PMFG is proposed by Tumminello et al., which is a network with triangular loops and four-element cliques. 2,27 In this paper, we aim to investigate the topological stability of stock market network which is filtered by the PMFG and MST algorithms. The topological stability is the ability of the network to resist structural or topological changes. 28 In the case of stock market network, the topological robustness is the ability of the network to resist the collapse of the listed companies (i.e., the removal of nodes). As briefed in the method proposed by Albert et al., 29 when the nodes are removed from network, clusters which connect to the removed nodes fall apart from the network. The removal of nodes can collapse the network and lead to catastrophic 1550161-2 Int. J. Mod. Phys. B Downloaded from www.worldscientific.com by UNIVERSITY OF GEORGIA on 08/12/15. For personal use only.

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