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The bi-directional h-index and B-core decomposition in directed networks

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  • Zhai, Li
  • Yan, Xiangbin
  • Zhang, Guojing

Abstract

Identifying important nodes is crucial for understanding network structure and function in the research of network science. A variety of methods are proposed to evaluate different quality aspects of node’s importance, in most cases ignoring the directed nature of links. In this paper, we introduce the bi-directional h-index to measure node’s importance, and the bi-directional k-core (B-core) decomposition for partition of network and detection dense subgraphs in directed networks. Considering the direction of links in directed networks, the bi-directional h-index and B-core decomposition can reflect the mutual influence of two kinds of reverse relations. By B-core decomposition, each node is assigned a bi-directional coreness to express its importance. The bi-directional h-index uses h-index algorithm for iterative calculation, and the directed degree centrality is its initial value, we prove that bi-directional coreness is its stable value. When the network is undirected, the bi-directional h-index is equivalent to the node’s h-index, and the B-core decomposition is equivalent to the classic graph-theoretic notion of k-core decomposition. Finally, we show the computation and convergence of bi-directional h-index and its difference from other methods in ranking of node’s importance in a real-world directed network.

Suggested Citation

  • Zhai, Li & Yan, Xiangbin & Zhang, Guojing, 2019. "The bi-directional h-index and B-core decomposition in directed networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 531(C).
    • Handle: RePEc:eee:phsmap:v:531:y:2019:i:c:s0378437119309574
    DOI: 10.1016/j.physa.2019.121715
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    Cited by:

    1. Wei, Shelia X. & Tong, Tong & Rousseau, Ronald & Wang, Wanru & Ye, Fred Y., 2022. "Relations among the h-, g-, ψ-, and p-index and offset-ability," Journal of Informetrics, Elsevier, vol. 16(4).

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