In this paper, we analyze information flows between communities of financial markets, represented as complex networks. Each community, typically corresponding to a business sector, represents a significant part of the financial market and the detection of interactions between communities is crucial in the analysis of risk spreading in the financial markets.

We show that the transfer entropy provides a coherent description of information flows in and between communities, also capturing non-linear interactions. Particularly, we focus on information transfer of rare events—typically large drops which can spread in the network. These events can be analyzed by Rényi transfer entropy, which enables to accentuate particular types of events.

We analyze transfer entropies between communities of the five largest financial markets and compare the information flows with the correlation network of each market. From the transfer entropy picture, we can also identify the non-linear interactions, which are typical in the case of extreme events. The strongest flows can be typically observed between specific types of business sectors—financial sectors is the most significant example.

J. Korbel, X Jiang, B. Zheng, Transfer Entropy between Communities in Complex Financial Networks, Entropy 21(11) (2019) 1124