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Generalized correlation dimension and heterogeneity of network spaces

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  • Nie, Chun-Xiao

Abstract

Many systems can be transformed into collections containing a large number of networks, such as dynamic networks. Defining metrics on a set of networks leads to analyzing a discrete metric space. In this study, we calculate the generalized correlation dimension of the network space and discuss the relationship between the dimension series and the heterogeneity index. Model-based analysis shows that generalized correlation dimension and GRI (Global Rényi Index) can be used as basic indicators of network space, and the space with evolutionary structure exhibits different dimension series in local and global perspectives. Furthermore, we analyze two types of network spaces, financial snapshot networks and temporal networks. Calculations show that real network spaces also exhibit heterogeneity and correspond to non-trivial dimension series. In particular, from a global perspective, the correlation dimensions of the analyzed network spaces are significantly smaller than the number of network nodes, implying that the intrinsic dimensions of these spaces are much smaller than those in the distance definition. This paper provides an analytical framework to characterize network space, which can be applied to describe space structure and compare different network sets.

Suggested Citation

  • Nie, Chun-Xiao, 2022. "Generalized correlation dimension and heterogeneity of network spaces," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    • Handle: RePEc:eee:chsofr:v:162:y:2022:i:c:s096007792200710x
    DOI: 10.1016/j.chaos.2022.112507
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    References listed on IDEAS

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    1. Nie, Chun-Xiao & Song, Fu-Tie & Li, Sai-Ping, 2016. "Rényi indices of financial minimum spanning trees," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 883-889.
    2. R. Mantegna, 1999. "Hierarchical structure in financial markets," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 11(1), pages 193-197, September.
    3. Nie, Chun-Xiao, 2017. "Correlation dimension of financial market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 473(C), pages 632-639.
    4. Tiago A. Schieber & Laura Carpi & Albert Díaz-Guilera & Panos M. Pardalos & Cristina Masoller & Martín G. Ravetti, 2017. "Quantification of network structural dissimilarities," Nature Communications, Nature, vol. 8(1), pages 1-10, April.
    5. C B Scott & Eric Mjolsness, 2021. "Graph diffusion distance: Properties and efficient computation," PLOS ONE, Public Library of Science, vol. 16(4), pages 1-44, April.
    6. Nie, Chun-Xiao & Song, Fu-Tie, 2019. "Global Rényi index of the distance matrix," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 902-915.
    7. Petter Holme, 2015. "Modern temporal network theory: a colloquium," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 88(9), pages 1-30, September.
    8. Bouchaud,Jean-Philippe & Potters,Marc, 2003. "Theory of Financial Risk and Derivative Pricing," Cambridge Books, Cambridge University Press, number 9780521819169, September.
    9. Eliazar, Iddo, 2011. "Randomness, evenness, and Rényi’s index," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(11), pages 1982-1990.
    10. Nie, Chun-Xiao & Song, Fu-Tie, 2018. "Analyzing the stock market based on the structure of kNN network," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 148-159.
    11. Peter Wills & François G Meyer, 2020. "Metrics for graph comparison: A practitioner’s guide," PLOS ONE, Public Library of Science, vol. 15(2), pages 1-54, February.
    12. Gutierrez Gomez, Efrain Leonardo & Delvenne, Jean-Charles, 2019. "Unsupervised network embeddings with node identity awareness," LIDAM Reprints CORE 3092, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    13. Nie, Chun-Xiao, 2019. "Applying correlation dimension to the analysis of the evolution of network structure," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 294-303.
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