The statistical nature of h-index of a network node

TL;DR

This paper provides a statistical interpretation of the h-index for network nodes using order statistics, leading to a versatile framework for developing more accurate and robust centrality measures.

Contribution

It introduces a new statistical perspective on the h-index and generalizes it to create a family of centrality indices for network importance assessment.

Findings

Statistical interpretation of h-index via order statistics.

Development of a new family of centrality indices.

Some new indices outperform h-index in accuracy and robustness.

Abstract

Evaluating the importance of a network node is a crucial task in network science and graph data mining. H-index is a popular centrality measure for this task, however, there is still a lack of its interpretation from a rigorous statistical aspect. Here we show the statistical nature of h-index from the perspective of order statistics, and we obtain a new family of centrality indices by generalizing the h-index along this direction. The theoretical and empirical evidences show that such a statistical interpretation enables us to obtain a general and versatile framework for quantifying the importance of a network node. Under this framework, many new centrality indices can be derived and some of which can be more accurate and robust than h-index. We believe that this research opens up new avenues for developing more effective indices for node importance quantification from a viewpoint that still remains unexplored.