  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 trades 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 null
model, a randomized version of the studied network sharing only the sizes and
interconnectivity between communities observed. We show that many topological
characteristics of the inferred networks are carried over the networks
generated by the null model. 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. We show that the framework presented here provides a good null
model representation of topological variations taking place in the market
during crises. Also, the general approach used in this work can be extended to
other systems.
