Identifying influential nodes is a hotspot issue in the research area of network science, and is of great significance in both theory and application. In recent studies, the H-index which was used to estimate the scientific impact of scientists was applied to identify influential nodes on complex networks. A fundamental relation, called the DHC theorem, was found among node degree, H-index, and coreness. In this paper, we extend the DHC theorem to directed and weighted networks, and proof that the DHC theorem is also valid. Then on this basis, this paper compares the ranking accuracy and resolution of the centralities in real weighted networks, and explores the role of weight ranking accuracy. Finally, by using the directed and weighted DHC theorem, the paper deeply analyzes the China Microblog retweet network between cities, assesses the online media influence of Chinese cities, and summarizes the information propagation patterns between users in different cities.%节点影响力排序是网络科学研究领域的热点问题,对该问题的研究极具理论意义与应用价值.最近有研究将原本用于衡量科学家科研影响力的H指数,引入到复杂网络中刻画节点的影响力,并发现节点的度、H指数和核数的内在联系,称为DHC定理.本文在原有研究基础上提出了有向含权网络上的H指数,并证明了DHC定理在有向含权网络中仍然成立.在此基础上,本文比较了这些节点中心性指标在含权网络上进行节点排序的准确性和分辨力,并考察了权重因素对排序准确性的影响.最后本文用含权有向网络上的DHC定理深入分析了中国城市间微博转发网络,对中国城市的在线媒体影响力进行排名,并总结了信息在不同城市用户之间的传播模式.
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