Correlation Research of Centralities on Complex Network by Statistical Learning

Abstract

In network theory and network analysis, indicators of centrality identify the most important vertices on complex networks. In this paper, we perform analysis on correlations of 13 centralities on ER random network and research how the Radial centralities interpret the Medial centralities adequately by statistical learning approaches such as linear regression, forward- and backward-stepwise selection and lasso. As a result, it is illustrated that some centralities on ER random networks with different connecting probability p always display strong correlations, and the Medial centrality can be interpreted by the Radial centralities. Furthermore, the linear regression is used to fit the relationship and retain some centralities to describe a medial centrality in our example, which will help to solve the problem that a centrality we don’t have a ready algorithm and compute difficultly. The methods proposed by statistical learning provide an alternative way to obtain better understanding of the centralities and reveal the relationship among them.