Finding modules and hierarchy in weighted financial network using transfer entropy

• We construct the information transfer network based on the transfer entropy.
• We analyze the modular structure with various time resolutions.
• We compare the results with modular structure obtained from the cross correlations.
• We show that the transfer entropy provides a better modular structure with higher value of modularity.

We study the modular structure of financial network based on the transfer entropy (TE). From the comparison with the obtained modular structure using the cross-correlation (CC), we find that TE and CC both provide well organized modular structure and the hierarchical relationship between each industrial group when the time scale of the measurement is less than one month. However, when the time scale of the measurement becomes larger than one month, we find that the modular structure from CC cannot correctly reflect the known industrial classification and their hierarchy. In addition the measured maximum modularity, QmaxQmax, for TE is always larger than that for CC, which indicates that TE is a better weight measure than CC for the system with asymmetric relationship.