Finding modules and hierarchy in weighted financial network using transfer entropy

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, _Qmax, 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.