LAUSR

Abstract In previous studies, the heterogeneity of complex networks has been extensively studied. In our study, the heterogeneity of distance matrices is studied based on the Renyi index of networks. We define a new metric and name it global Renyi index ( G R I ), and prove several properties. In particular, the G R I value of the distance matrix corresponding to the evenly distributed point set in the Euclidean space is zero. Some model data were used to clarify the geometric meanings of G R I , and then we studied the G R I value of financial data. The results show that the G R I value in the real market changes drastically and is significantly different from the G R I value of the model-generated data. These results suggest that the proposed concept ( G R I ) is meaningful to the study distance matrix and provides a new perspective based on the network.