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Large directed-graph layout and its application to a million-firms economic network

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Abstract

This study proposes a practical directed-graph drawing method that can be applied to large-scale relational data by modifying multidimensional scaling (MDS). We modified the mutual distance between the nodes to incorporate the link direction information in the distance matrix, from which the coordinate of the vertex is obtained. As the application of our method, we visualized the big data of real economy of Japan which includes a million companies and millions of relations, and we particularly deal with how firms are connected. Moreover, we discovered interesting features of the economic network. Firms are connected by links into tightly knit groups with high intragroup density and low intergroup connectivity community structures. We also found that the features of community structures are specific to individual industrial sectors, such as manufacturing, retail, wholesale, and construction.

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Notes

  1. This data is provided by the Research Institute of Economy, Trade and Industry (RIETI).

  2. There are 3% of back-and-forth edges, which means this score has an upper bound of 97%.

  3. Some tree graphs can also suffer from this problem. See Fig. 4.

References

  • Barnes J, Hut P (1986) A hierarchical O(N log N) force-calculation algorithm. Nature 324(6096):446–449

    Article  Google Scholar 

  • Brandes U, Pich C (2007) Eigensolver methods for progressive multidimensional scaling of large data. In: Proceedings of 14th symposium on graph drawing (GD), Lecture Notes in Computer Science, vol 4372, pp 42–53

  • Fujiwara Y, Terai M, Fujita Y, Souma W (2016) Debtrank analysis of financial distress propagation on a production network in Japan. RIETI Discussion Paper Series 16-E-046

  • Gansner ER, Koutsofios E, North SC, Vo GP (1993) A technique for drawing directed graphs. IEEE Trans Softw Eng 19(3):214–230

    Article  Google Scholar 

  • Hadany R, Harel D (2001) A multi-scale algorithm for drawing graphs nicely. Discrete Appl Math 113(1):3–21

    Article  Google Scholar 

  • Hu Y (2006) Efficient, high-quality force-directed graph. Math J 10(1):37–71

    Google Scholar 

  • Iino T, Iyetomi H (2015) The economics of interfirm networks, chap. Community Structure of a Large-Scale Production Network in Japan. Springer, Japan

  • Japan Standard Industrial Classification (2007) (Rev. 12). http://www.stat.go.jp/english/index/seido/sangyo/index07.htm

  • Quigley A, Eades P (2000) Fade: graph drawing, clustering, and visual abstraction. In: Proceedings of the 8th symposium on graph drawing (GD), Lecture Notes in Computer Science, vol 1984, p 197210

  • Sugiyama K, Misue K (1995) Graph drawing by the magnetic spring model. J Vis Lang Comput 6:217231

    Article  Google Scholar 

  • Tamassia R (2013) Handbook of graph drawing and visualization. CRC Press, USA

    Google Scholar 

  • Tokyo Shoko Research, Ltd (2016) Tokyo, Japan. http://www.tsr-net.co.jp

Download references

Acknowledgements

This work was partially supported by Grant-in-Aid for Scientific Research (KAKENHI) Grant Numbers 25282094 by JSPS. We are grateful to Atsushi Kawai (K&F Computing, Inc.) for sharing the code of the Barnes-Hut algorithm This study was conducted as a part of the project “Price Network and Dynamics of Small and Medium Enterprises” undertaken at the Research Institute of Economy, Trade and Industry (RIETI). We are also grateful to Hiroshi Iyetomi, a member of the project, for giving us the reference (Iino and Iyetomi 2015). The authors thank the Yukawa Institute for Theoretical Physics at Kyoto University. Discussions during the YITP workshop YITP-W-15-15 on “Econophysics 2015” were useful to complete this work.

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Authors and Affiliations

  1. Turnstone Research Institute, Kamakura, Japan

    Yuji Fujita

  2. University of Hyogo, Kobe, Japan

    Yoshi Fujiwara

  3. Nihon University, Funabashi, Japan

    Wataru Souma

Authors
  1. Yuji Fujita
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  2. Yoshi Fujiwara
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  3. Wataru Souma
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Corresponding author

Correspondence to Yuji Fujita.

Additional information

The authors thank the Yukawa Institute for Theoretical Physics at Kyoto University. Discussions during the YITP workshop YITP-W-15-15 on “Econophysics 2015” were useful to complete this work.

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Fujita, Y., Fujiwara, Y. & Souma, W. Large directed-graph layout and its application to a million-firms economic network. Evolut Inst Econ Rev 13, 397–408 (2016). https://doi.org/10.1007/s40844-016-0059-9

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  • DOI: https://doi.org/10.1007/s40844-016-0059-9

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