Spectrum, Intensity and Coherence in Weighted Networks of a Financial Market

We construct a correlation matrix based financial network for a set of New York Stock Exchange (NYSE) traded stocks with stocks corresponding to nodes and the links between them added one after the other, according to the strength of the correlation between the nodes. The eigenvalue spectrum of the correlation matrix reflects the structure of the market, which also shows in the cluster structure of the emergent network. The stronger and more compact a cluster is, the earlier the eigenvalue representing the corresponding business sector occurs in the spectrum. On the other hand, if groups of stocks belonging to a given business sector are considered as a fully connected subgraph of the final network, their intensity and coherence can be monitored as a function of time. This approach indicates to what extent the business sector classifications are visible in market prices, which in turn enables us to gauge the extent of group-behaviour exhibited by stocks belonging to a given business sector.Comment: 10 pages, 3 figure

An Outlook on Correlations in Stock Prices

We present an outlook of the studies on correlations in the price timeseries of stocks, discussing the construction and applications of "asset tree". The topic discussed here should illustrate how the complex economic system (financial market) enrichens the list of existing dynamical systems that physicists have been studying for long.Comment: 6 pages, RevTeX format. To appear in the Conference Proceedings of ECONOPHYS-KOLKATA II: International Workshop on Econophysics of Stock Markets and Minority Games", February 14-17, 2006, SINP, Kolkata, as a book chapter in Eds. A. Chatterjee and B.K. Chakrabarti, Econophysics of Stock and other Markets, (Springer-Verlag (Italia), Milan, 2006

Spectral and network methods in the analysis of correlation matrices of stock returns

Correlation matrices inferred from stock return time series contain information on the behaviour of the market, especially on clusters of highly correlating stocks. Here we study a subset of New York Stock Exchange (NYSE) traded stocks and compare three different methods of analysis: i) spectral analysis, i.e. investigation of the eigenvalue-eigenvector pairs of the correlation matrix, ii) asset trees, obtained by constructing the maximal spanning tree of the correlation matrix, and iii) asset graphs, which are networks in which the strongest correlations are depicted as edges. We illustrate and discuss the localisation of the most significant modes of fluctuation, i.e. eigenvectors corresponding to the largest eigenvalues, on the asset trees and graphs.Comment: 6 pages, 2 figure

Increasing market efficiency: Evolution of cross-correlations of stock returns

We analyse the temporal changes in the cross correlations of returns on the New York Stock Exchange. We show that lead-lag relationships between daily returns of stocks vanished in less than twenty years. We have found that even for high frequency data the asymmetry of time dependent cross-correlation functions has a decreasing tendency, the position of their peaks are shifted towards the origin while these peaks become sharper and higher, resulting in a diminution of the Epps effect. All these findings indicate that the market becomes increasingly efficient.Comment: 12 pages, 8 figures, accepted to Physica

Communities in Networks

We survey some of the concepts, methods, and applications of community detection, which has become an increasingly important area of network science. To help ease newcomers into the field, we provide a guide to available methodology and open problems, and discuss why scientists from diverse backgrounds are interested in these problems. As a running theme, we emphasize the connections of community detection to problems in statistical physics and computational optimization.Comment: survey/review article on community structure in networks; published version is available at http://people.maths.ox.ac.uk/~porterm/papers/comnotices.pd