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.

翻译：在网络科学与图数据挖掘中，评估网络节点重要性是一项关键任务。h指数是该任务中常用的中心性度量指标，然而目前仍缺乏从严格统计学角度对其的解读。本文从顺序统计量的视角揭示了h指数的统计本质，并沿此方向通过推广h指数获得了一类新的中心性指标。理论与实证证据表明，这种统计解释使我们能够构建一个通用且灵活的网络节点重要性量化框架。在该框架下可衍生出多种新型中心性指标，其中部分指标在准确性与鲁棒性上优于h指数。我们相信，这项研究从尚未被探索的视角为开发更有效的节点重要性量化指标开辟了新路径。