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.

许多系统可以转化为包含大量网络的集合，例如动态网络。在一组网络上定义度量会导致分析离散的度量空间。在本研究中，我们计算了网络空间的广义相关维度，并讨论了维度序列与异质性指标之间的关系。基于模型的分析表明，广义相关维度和$GR我$（Global Rényi Index）可以作为网络空间的基本指标，具有演化结构的空间在局部和全局视角下表现出不同的维度序列。此外，我们分析了两种类型的网络空间，金融快照网络和时间网络。计算表明，真实的网络空间也表现出异质性，并且对应于非平凡的维度序列。特别是，从全局角度来看，分析的网络空间的相关维度明显小于网络节点的数量，这意味着这些空间的内在维度远小于距离定义中的维度。本文提供了一个表征网络空间的分析框架，可用于描述空间结构和比较不同的网络集。