On the Modular Dynamics of Financial Market Networks

The financial market is a complex dynamical system composed of a large variety of intricate relationships between several entities, such as banks, corporations and institutions. At the heart of the system lies the stock exchange mechanism, which establishes a time-evolving network of transactions among companies and individuals. Such network can be inferred through correlations between time series of companies stock prices, allowing the overall system to be characterized by techniques borrowed from network science. Here we study the presence of communities in the inferred stock market network, and show that the knowledge about the communities alone can provide a nearly complete representation of the system topology. This is done by defining a simple random model sharing only the sizes and interconnectivity between communities observed in the time-evolving stock market network. We show that many topological characteristics of the inferred networks are preserved in the modeled networks. In particular, we find that in periods of instability, such as during a financial crisis, the network strays away from a state of well-defined community structure to a much more uniform topological organization. This behavior is found to be strongly related to the recently formalized von Neumann entropy for graphs. In addition, the community structure of the market network is used to define a community-based model of crisis periods observed in the market. We show that such model provides a good representation of topological variations taking place in the market during the crises. The general approach used in this work can be extended to other systems.