IDEAS home Printed from https://ideas.repec.org/a/spr/jcsosc/v2y2019i1d10.1007_s42001-019-00031-1.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s42001-019-00031-1
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s42001-019-00031-1?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Venera Timiryanova & Konstantin Grishin & Dina Krasnoselskaya, 2020. "Spatial Patterns of Production-Distribution-Consumption Cycle: The Specifics of Developing Russia," Economies, MDPI, vol. 8(4), pages 1-18, October.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Daisuke Sato & Yuichi Ikeda & Shuichi Kawai & Maxmilian Schich, 2020. "The sustainability and the survivability of Kyoto’s traditional craft industry revealed from supplier-customer network," PLOS ONE, Public Library of Science, vol. 15(11), pages 1-23, November.
    3. FUJIWARA Yoshi & INOUE Hiroyasu & YAMAGUCHI Takayuki & AOYAMA Hideaki & TANAKA Takuma & KIKUCHI Kentaro, 2021. "Money Flow Network Among Firms' Accounts in a Regional Bank of Japan," Discussion papers 21005, Research Institute of Economy, Trade and Industry (RIETI).
    4. Hiromitsu Goto & Wataru Souma & Mari Jibu & Yuichi Ikeda, 2020. "Multilayer Network Analysis of the Drug Pipeline in the Global Pharmaceutical Industry," Papers 2003.04620, arXiv.org.
    5. Kumar, Ashish & Chakrabarti, Anindya S. & Chakraborti, Anirban & Nandi, Tushar, 2021. "Distress propagation on production networks: Coarse-graining and modularity of linkages," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 568(C).
    6. Venera Maratovna Timiryanova, 2019. "Evaluation of Supply Chain Using Hierarchical Analysis," International Journal of Economics & Business Administration (IJEBA), International Journal of Economics & Business Administration (IJEBA), vol. 0(3), pages 178-186.
    7. C'elestin Coquid'e & Jos'e Lages & Dima L. Shepelyansky, 2023. "Prospects of BRICS currency dominance in international trade," Papers 2305.00585, arXiv.org.
    8. Corrado Di Guilmi & Yoshi Fujiwara, 2020. "Does the supply network shape the firm size distribution? The Japanese case," CAMA Working Papers 2020-66, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    9. SATO Daisuke & IKEDA Yuichi & KAWAI Shuichi & Maxmilian SCHICH, 2020. "Supply-Chain Network Analysis of Kyoto's Traditional Craft Industry," Discussion papers 20044, Research Institute of Economy, Trade and Industry (RIETI).
    10. Yuji Fujita & Yoshi Fujiwara & Wataru Souma, 2019. "Macroscopic features of production network and sequential graph drawing," Evolutionary and Institutional Economics Review, Springer, vol. 16(1), pages 183-199, June.
    11. Abhijit Chakraborty & Hiroyasu Inoue & Yoshi Fujiwara, 2020. "Economic complexity of prefectures in Japan," PLOS ONE, Public Library of Science, vol. 15(8), pages 1-13, August.
    12. Tembo Nakamoto & Abhijit Chakraborty & Yuichi Ikeda, 2019. "Identification of Key Companies for International Profit Shifting in the Global Ownership Network," Papers 1904.12397, arXiv.org.
    13. Matthias Raddant & Hiroshi Takahashi, 2022. "Corporate boards, interorganizational ties and profitability: the case of Japan," Empirical Economics, Springer, vol. 62(3), pages 1365-1406, March.
    14. Hideaki Aoyama, 2021. "XRP Network and Proposal of Flow Index," Papers 2106.10012, arXiv.org.
    15. C'elestin Coquid'e & Leonardo Ermann & Jos'e Lages & D. L. Shepelyansky, 2019. "Influence of petroleum and gas trade on EU economies from the reduced Google matrix analysis of UN COMTRADE data," Papers 1903.01820, arXiv.org.
    16. Abhijit Chakraborty & Yuichi Ikeda, 2020. "Bow-tie structure and community identification of global supply chain network," Papers 2003.02343, arXiv.org.
    17. Yoshi Fujiwara & Hiroyasu Inoue & Takayuki Yamaguchi & Hideaki Aoyama & Takuma Tanaka, 2020. "Money flow network among firms' accounts in a regional bank of Japan," Papers 2007.14630, arXiv.org, revised Jul 2020.
    18. KICHIKAWA Yuichi & IINO Takashi & IYETOMI Hiroshi & INOUE Hiroyasu, 2019. "Hierarchical and Circular Flow Structure of the Interfirm Transaction Network in Japan," Discussion papers 19063, Research Institute of Economy, Trade and Industry (RIETI).
    19. Abhijit Chakraborty & Hiroyasu Inoue & Yoshi Fujiwara, 2020. "Economic complexity of prefectures in Japan," Papers 2002.05785, arXiv.org, revised Aug 2020.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:jcsosc:v:2:y:2019:i:1:d:10.1007_s42001-019-00031-1. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.