Global Rényi index of the distance matrix
| Autor: | Fu-Tie Song, Chun-Xiao Nie |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Statistics and Probability
Discrete mathematics Euclidean space Zero (complex analysis) Statistical and Nonlinear Physics Complex network 01 natural sciences 010305 fluids & plasmas Perspective (geometry) Distance matrix 0103 physical sciences Metric (mathematics) 010306 general physics Value (mathematics) Distance matrices in phylogeny Mathematics |
| Zdroj: | Physica A: Statistical Mechanics and its Applications. 514:902-915 |
| ISSN: | 0378-4371 |
| DOI: | 10.1016/j.physa.2018.09.112 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect