Statistical analysis of financial networks

Massive datasets arise in a broad spectrum of scienti$c, engineering and commercial applications. In many practically important cases, a massive dataset can be represented as a very large graph with certain attributes associated with its vertices and edges. Studying the structure of this graph is essential for understanding the structural properties of the application it represents. Well-known examples of applying this approach are the Internet graph, the Web graph, and the Call graph. It turns out that the degree distributions of all these graphs can be described by the power-law model. Here we consider another important application—a network representation of the stock market. Stock markets generate huge amounts of data, which can be used for constructing the market graph re9ecting the market behavior. We conduct the statistical analysis of this graph and show that it also follows the power-law model. Moreover, we detect cliques and independent sets in this graph. These special formations have a clear practical interpretation, and their analysis allows one to apply a new data mining technique of classifying $nancial instruments based on stock prices data, which provides a deeper insight into the internal structure of the stock market. c © 2004 Elsevier B.V. All rights reserved.