Winner-Take-All Correlation-Based Complex Networks for Modeling Stock Market and Degree-Based Indexes

Complex networks are constructed to study correlations between the closing prices for all US stocks that were traded from July 1, 2005 to August 30, 2007. The nodes are the stocks, and the connections are determined by cross correlations of the variations of the stock prices and price returns within a chosen period of time. Specifically, a winner-take-all approach is used to determine if two nodes are connected by an edge. The network thus formed is a full network of stock prices giving full information about their interdependence. We find that the distribution of the number of connections follows a power law. Such power-law distribution is also found in several variations of complex networks formed by considering price returns and trading volumes. The results from this work clearly suggest that the variation of stock prices are strongly influenced by a relatively small number of stocks. We propose a new approach for selecting stocks for inclusion in stock indices and compare it with existing approaches.