The network heterogeneity has been defined in various ways in the literature [1].
If we carefully analyse the heterogeneity measures proposed in the literature, it becomes clear that two different aspects of a complex network can be quantified through a heterogeneity measure, as
where \(⟨k⟩\) represents the average degree in the network. Though this is still one of the popular measures of heterogeneity, its applicability is mainly limited to RGs where one can effectively define an average \(k\).
They are the diversity in node degrees and the diversity in the structure of the network. For example, the initial attempts to measure the heterogeneity try to capture the diversity in the node degrees of the network and were mainly motivated by the RG theory. The first person to propose a measure of heterogeneity was Snijders [2] in the context of social networks and it was modified by Bell [3] as the variance of node degrees:
参考文献：
- Jacob R , Harikrishnan K P , Misra R , et al. Measure for degree heterogeneity in complex networks and its application to recurrence network analysis[J]. Royal Society Open Science, 2017, 4(1):160757.
- Snijders TAB. 1981The degree variance: an index of graph heterogeneity. Soc. Netw. 3, 163–174.
- Bell FK. 1992A note on the irregularity of graphs. Linear Algebra Appl. 161, 45–54.