Coarse Graining on Financial Correlation Networks

Community structure detection is an important and valuable task in financial network studies as it forms the basis of many statistical applications such prediction, risk analysis, recommendation. Financial networks have a natural multi-grained that leads to different community structures at levels. However, few pay attention these multi-part features networks. In this study, we present geometric coarse graining method based on Voronoi regions network. Rather than studying dense network, perform our analysis triangular maximally filtering Such filtered topology emerges efficient approach because keeps local clustering coefficients steady underlies geometry. Moreover, order capture changes grains geometry throughout stress, study Haantjes curvatures paths are farthest from center each regions. We performed representation comprising stock market indices BIST (Borsa Istanbul), FTSE100 (London Stock Exchange), Nasdaq-100 Index (NASDAQ), across three crisis periods. Our results indicate there remarkable grains.