Generalized correlation dimension and heterogeneity of network spaces

Chun-Xiao Nie

Chaos, Solitons & Fractals, 2022, vol. 162, issue C

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.

Keywords: Network space; Correlation dimension; Multifractal; Global Rényi Index (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:162:y:2022:i:c:s096007792200710x

DOI: 10.1016/j.chaos.2022.112507

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