Principal centrality measures: a comprehensive approach to the Spanish stocks market
Keywords:Social Network Analysis, Centrality Measures
In social network analysis, for determining the relevance or significance of a node in the network, several node centrality measures are often used such as degree centrality, betwenness centrality, closeness centrality, eigenvector, subgraph and page rank centrality. In this paper we apply a principal components analysis over the traditional centrality measures for obtaining an overall single metric that combines the best attributes of the traditional centrality measures and permits to detect relevant nodes in the network. Concretely, a detailed study of the Spanish stocks market will be used for demonstrating the advantages of this approach.
 G. Bonanno, G. Caldarelli, F. Lillo and R. N. Mantegna, Topology of correlation-based minimal spanning trees in real and model market, Physical Review E, vol. 68, pp. 046130-046133, 2003.
 E. Estrada,, and J. A. Rodriguez Velazquez, Subgraph centrality in complex networks, Physical Review E 71 (2005) 056103.
 Estrada, E., and Orjan Bodin, Using network centrality measures to manage landscape connectivity, Ecological Applications, 18(7), (2008) pp. 1810â€“1825.
 L. C. Freeman, Centrality in networks: I. Conceptual clarification, Social Networks, vol. 1,(1979) pp. 251-239.
 L. C. Freeman, A set of measures of centrality based on betweenness. Sociometry, 40(1), (1977) 35-41.
 I. T. Jolliffe, Principal Component Analysis, 2nd ed. Springer, New York, 2002.
 J.B. Kruskal, On the shortest spanning subtree of a graph and the travelling salesman problem. American Mathematical Society, vol. 7, no. 1, (1956) pp. 48-50.
 G.S. Lee, Maman A. Djauhari, An Overall Centrality Measure: The Case of U.S Stock Market. International Journal of Basic and Applied Science, Vol 12, (2012).
 R.N. Mantegna, Hierarchical Structure in Financial Markets, European Physical Journal B, 11, (1999) 193-197.
 J. P. Onnela, A. Chakraborti, K. Kaski, J. Kertâ€™esz and A. Kanto, Dynamics of market correlations: Taxonomy and portfolio analysis, Physical Review E, vol. 68, (2003) pp. 056110(1)-056110(12).
 S. Sharif, M. A. Djauhari, A Proposed Centrality Measure: The Case of Stocks Traded at Bursa Malaysia. Modern Applied Science; Vol. 6, No. 10 (2012).
 V. Tola, F. Lillo, M. Gallegati and R. N. Mantegna, Cluster analysis for portfolio optimization, Journal of Economic Dynamic and Control, vol. 32, (2008) pp. 235-258.
 M. Tumminello, T. Aste, T. D. Matteo and R. N. Mantegna, A tool for filtering information in complex systems,â€ Proceedings of the National Academy of Sciences, vol. 102, (2005) pp. 10421-10426.
 D.B. West, Introduction to Graph Theory (2nd ed.). Englewood Cliffs, NJ: Prentice-Hall. 2000.