IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v176y2023ics0960077923010081.html
   My bibliography  Save this article

The average shortest distance of three colored substitution networks

Author

Listed:
  • Hu, Zhongren
  • Wu, Bo

Abstract

The circuit is a system composed of multiple components. The module of the circuit refers to the combination of components with similar functions in the circuit to form a module. In order to study the transmission efficiency of the circuit module, this paper projects it into three color substitution networks. The three colors are blue, red and green, respectively, representing a combination of circuit modules, based on certain substitution rules during the construction of the network. This paper studies the average shortest path between any two nodes in the circuit module, which reflects the transmission efficiency of the network. We calculate the shortest distance between the initial nodes of different modules and obtain the average shortest distance across the entire network based on the substitute iteration rules generated by the network. The results show that with the continuous expansion of the network, the average shortest distance is sub-linearly fitted to the network order.

Suggested Citation

  • Hu, Zhongren & Wu, Bo, 2023. "The average shortest distance of three colored substitution networks," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    • Handle: RePEc:eee:chsofr:v:176:y:2023:i:c:s0960077923010081
    DOI: 10.1016/j.chaos.2023.114107
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077923010081
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2023.114107?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. Barabási, Albert-László & Albert, Réka & Jeong, Hawoong, 2000. "Scale-free characteristics of random networks: the topology of the world-wide web," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 281(1), pages 69-77.
    2. Duncan J. Watts & Steven H. Strogatz, 1998. "Collective dynamics of ‘small-world’ networks," Nature, Nature, vol. 393(6684), pages 440-442, June.
    3. Yuke Huang & Cheng Zeng & Hanxiong Zhang & Yumei Xue, 2022. "Average Trapping Time Of Honeypots On Weighted Random Fractal Networks," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(07), pages 1-9, November.
    4. Donglei, Tang & Weiyi, SU, 2005. "The Laplacian on the level 3 Sierpinski gasket via the method of averages," Chaos, Solitons & Fractals, Elsevier, vol. 23(4), pages 1201-1209.
    5. Carletti, Timoteo & Righi, Simone, 2010. "Weighted Fractal Networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(10), pages 2134-2142.
    6. Meifeng Dai & Changxi Dai & Huiling Wu & Xianbin Wu & Wenjing Feng & Weiyi Su, 2019. "The trapping problem and the average shortest weighted path of the weighted pseudofractal scale-free networks," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 30(01), pages 1-17, January.
    7. Dai, Meifeng & Chen, Dandan & Dong, Yujuan & Liu, Jie, 2012. "Scaling of average receiving time and average weighted shortest path on weighted Koch networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(23), pages 6165-6173.
    8. Li, Ziyu & Yao, Jialing & Wang, Qin, 2019. "Fractality of multiple colored substitution networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 402-408.
    9. Dai, Meifeng & Dai, Changxi & Ju, Tingting & Shen, Junjie & Sun, Yu & Su, Weiyi, 2019. "Mean first-passage times for two biased walks on the weighted rose networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 268-278.
    10. A. Barrat & M. Weigt, 2000. "On the properties of small-world network models," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 13(3), pages 547-560, February.
    11. Wu, Bo & Zhang, Zhizhuo, 2020. "The average trapping time on a half Sierpinski Gasket," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    12. Niu, Min & Song, Shuaishuai, 2018. "Scaling of average weighted shortest path and average receiving time on the weighted Cayley networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 707-717.
    13. Rui Ding & Norsidah Ujang & Hussain Bin Hamid & Mohd Shahrudin Abd Manan & Rong Li & Safwan Subhi Mousa Albadareen & Ashkan Nochian & Jianjun Wu, 2019. "Application of Complex Networks Theory in Urban Traffic Network Researches," Networks and Spatial Economics, Springer, vol. 19(4), pages 1281-1317, 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. Yang, Jinling & Chen, Zhiwei & Criado, Regino & Zhang, Shenggui, 2024. "A mathematical framework for shortest path length computation in multi-layer networks with inter-edge weighting and dynamic inter-edge weighting: The case of the Beijing bus network, China," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).

    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. Dai, Meifeng & Dai, Changxi & Ju, Tingting & Shen, Junjie & Sun, Yu & Su, Weiyi, 2019. "Mean first-passage times for two biased walks on the weighted rose networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 268-278.
    2. Huang, Da-Wen & Yu, Zu-Guo & Anh, Vo, 2017. "Multifractal analysis and topological properties of a new family of weighted Koch networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 469(C), pages 695-705.
    3. Zong, Yue & Dai, Meifeng & Wang, Xiaoqian & He, Jiaojiao & Zou, Jiahui & Su, Weiyi, 2018. "Network coherence and eigentime identity on a family of weighted fractal networks," Chaos, Solitons & Fractals, Elsevier, vol. 109(C), pages 184-194.
    4. Pereira, F.B. & Ferreira, R.S. & Alencar, D.S.M. & Alves, T.F.A. & Alves, G.A. & Lima, F.W.S. & Macedo-Filho, A., 2024. "Social dilemmas, network reciprocity, and small-world property," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 655(C).
    5. Rui Ding, 2019. "The Complex Network Theory-Based Urban Land-Use and Transport Interaction Studies," Complexity, Hindawi, vol. 2019, pages 1-14, June.
    6. Matthias Lischke & Benjamin Fabian, 2016. "Analyzing the Bitcoin Network: The First Four Years," Future Internet, MDPI, vol. 8(1), pages 1-40, March.
    7. Zhang Zhang & Arsham Ghavasieh & Jiang Zhang & Manlio Domenico, 2025. "Coarse-graining network flow through statistical physics and machine learning," Nature Communications, Nature, vol. 16(1), pages 1-11, December.
    8. Ye, Dandan & Dai, Meifeng & Sun, Yu & Su, Weiyi, 2017. "Average weighted receiving time on the non-homogeneous double-weighted fractal networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 473(C), pages 390-402.
    9. Dai, Meifeng & Shao, Shuxiang & Su, Weiyi & Xi, Lifeng & Sun, Yanqiu, 2017. "The modified box dimension and average weighted receiving time of the weighted hierarchical graph," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 475(C), pages 46-58.
    10. Sun, Yu & Dai, Meifeng & Xi, Lifeng, 2014. "Scaling of average weighted shortest path and average receiving time on weighted hierarchical networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 407(C), pages 110-118.
    11. repec:plo:pone00:0121946 is not listed on IDEAS
    12. Manajit Chakraborty & Maksym Byshkin & Fabio Crestani, 2020. "Patent citation network analysis: A perspective from descriptive statistics and ERGMs," PLOS ONE, Public Library of Science, vol. 15(12), pages 1-28, December.
    13. Zhao, Star X. & Rousseau, Ronald & Ye, Fred Y., 2011. "h-Degree as a basic measure in weighted networks," Journal of Informetrics, Elsevier, vol. 5(4), pages 668-677.
    14. Li, Chunguang, 2009. "Memorizing morph patterns in small-world neuronal network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(2), pages 240-246.
    15. Citera, Emanuele & Gouri Suresh, Shyam & Setterfield, Mark, 2023. "The network origins of aggregate fluctuations: A demand-side approach," Structural Change and Economic Dynamics, Elsevier, vol. 64(C), pages 111-123.
    16. Hao, Xiaoqing & An, Haizhong & Jiang, Meihui & Sun, Xiaoqi, 2024. "Supply shock propagation in the multi-layer network of global steel product chain: Additive effect of trade and production," Resources Policy, Elsevier, vol. 89(C).
    17. Pascal Billand & Christophe Bravard & Sudipta Sarangi, 2013. "Modeling resource flow asymmetries using condensation networks," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(3), pages 537-549, September.
    18. Huan Wang & Chuang Ma & Han-Shuang Chen & Ying-Cheng Lai & Hai-Feng Zhang, 2022. "Full reconstruction of simplicial complexes from binary contagion and Ising data," Nature Communications, Nature, vol. 13(1), pages 1-10, December.
    19. Vinayak, & Raghuvanshi, Adarsh & kshitij, Avinash, 2023. "Signatures of capacity development through research collaborations in artificial intelligence and machine learning," Journal of Informetrics, Elsevier, vol. 17(1).
    20. Seabrook, Isobel E. & Barucca, Paolo & Caccioli, Fabio, 2021. "Evaluating structural edge importance in temporal networks," LSE Research Online Documents on Economics 112515, London School of Economics and Political Science, LSE Library.
    21. Supriya Tiwari & Pallavi Basu, 2024. "Quasi-randomization tests for network interference," Papers 2403.16673, arXiv.org, revised Oct 2024.

    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:eee:chsofr:v:176:y:2023:i:c:s0960077923010081. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.