Bi-directional h-index: A new measure of node centrality in weighted and directed networks

This paper builds an index family, named bi-directional h-index, to measure node centrality in weighted directed networks. Bi-directional h-index takes the directed degree centrality as the initial value and iteratively uses more network information to update the node's importance. We prove the convergence of the iterative process after finite iterations and introduce an asynchronous updating process that provides a decentralized, local method to calculate the bi-directional h-index in large-scale networks and dynamic networks. The theoretical analysis manifests that the bi-directional h-index is feasible and significant for establishing a greater conceptual framework that includes some existing index concepts, such as lobby index, node's h-index, c-index and iterative c-index. An example using journal citation networks indicates that the bi-directional h-index is different from directed degree centrality, directed node strength, directed h-degree and the HITS algorithm in ranking node importance. It is irreplaceable and can reflect these measures of node's importance.