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Visualization of a directed network with focus on its hierarchy and circularity

Author

Listed:
  • Yuichi Kichikawa

    (Niigata University)

  • Takashi Iino

    (Niigata University)

  • Hiroshi Iyetomi

    (Niigata University)

  • Hiroyasu Inoue

    (The University of Hyogo)

Abstract

The spring-electric model is a useful tool to visualize a large-scale complex network. However, information on the flow of directed network may not be properly reflected because links are basically treated as undirected. Here, we propose a new visualization method with an explicit account of network flow structure information by combining Helmholtz–Hodge decomposition and the spring-electric model. We then demonstrate its effectiveness by adopting actual Japanese production flow network as a test ground. The Helmholtz–Hodge decomposition enables us to break down flow on a directed network into two flow components: potential flow and circular flow. The potential flow between a pair of nodes is given by difference of their potentials, and hence, the potential of a node shows its hierarchical position in a network. On the other hand, the circular flow component illuminates feedback loops built in a network. We also identify dominant clusters of firms forming feedback loops by applying a flow-based community detection method to the extracted circular flow network. We find that both hierarchical and loop structures coexist within the major industries such as construction, manufacturing, and wholesales.

Suggested Citation

  • Yuichi Kichikawa & Takashi Iino & Hiroshi Iyetomi & Hiroyasu Inoue, 2019. "Visualization of a directed network with focus on its hierarchy and circularity," Journal of Computational Social Science, Springer, vol. 2(1), pages 15-23, January.
    • Handle: RePEc:spr:jcsosc:v:2:y:2019:i:1:d:10.1007_s42001-019-00031-1
    DOI: 10.1007/s42001-019-00031-1
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    References listed on IDEAS

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    1. Yuji Fujita & Yoshi Fujiwara & Wataru Souma, 2016. "Large directed-graph layout and its application to a million-firms economic network," Evolutionary and Institutional Economics Review, Springer, vol. 13(2), pages 397-408, December.
    2. Abhijit Chakraborty & Yuichi Kichikawa & Takashi Iino & Hiroshi Iyetomi & Hiroyasu Inoue & Yoshi Fujiwara & Hideaki Aoyama, 2018. "Hierarchical communities in the walnut structure of the Japanese production network," PLOS ONE, Public Library of Science, vol. 13(8), pages 1-25, August.
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