IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v556y2020ics0378437120303733.html
   My bibliography  Save this article

Two cumulative distributions for scale-freeness of dynamic networks

Author

Listed:
  • Wang, Xiaomin
  • Yao, Bing

Abstract

It is well-known that the scale-free networks are ubiquitous in nature and society and have been one of the hotspot topic in complex networks. Recently, scholars presented a large quantity of scale-free networks by calculating cumulative distribution. The purpose of this paper is to discuss the relationship between two cumulative distributions, namely, cumulative distribution, edge-cumulative distribution. Here, firstly, we introduce a relationship between degree distribution and cumulative distribution. Secondly, we introduce the definition of cumulative distribution and edge-cumulative distribution, and compare the relationship between them. Thirdly, we apply algorithmic techniques to construct three deterministic networks, calculate their cumulative distribution and edge-cumulative distribution, and analyze the relationship between cumulative distribution and edge-cumulative distribution. Finally, we offer some open problems for future research in order to understand the interplay between the degree distribution, cumulative distribution and edge-cumulative distribution.

Suggested Citation

  • Wang, Xiaomin & Yao, Bing, 2020. "Two cumulative distributions for scale-freeness of dynamic networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 556(C).
    • Handle: RePEc:eee:phsmap:v:556:y:2020:i:c:s0378437120303733
    DOI: 10.1016/j.physa.2020.124747
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437120303733
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2020.124747?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. Zhang, Zhongzhi & Rong, Lili & Comellas, Francesc, 2006. "High-dimensional random Apollonian networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 364(C), pages 610-618.
    2. Barabási, A.L & Jeong, H & Néda, Z & Ravasz, E & Schubert, A & Vicsek, T, 2002. "Evolution of the social network of scientific collaborations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 311(3), pages 590-614.
    3. Diego Garlaschelli & Guido Caldarelli & Luciano Pietronero, 2003. "Universal scaling relations in food webs," Nature, Nature, vol. 423(6936), pages 165-168, May.
    4. Wu, Jieyu & Shao, Xinyu & Li, Jinhang & Huang, Gang, 2012. "Scale-free properties of information flux networks in genetic algorithms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1692-1701.
    Full references (including those not matched with items on IDEAS)

    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. Fang, Yinhai & Xu, Haiyan & Perc, Matjaž & Tan, Qingmei, 2019. "Dynamic evolution of economic networks under the influence of mergers and divestitures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 89-99.
    2. Jacob Wood & Gohar Feroz Khan, 2015. "International trade negotiation analysis: network and semantic knowledge infrastructure," Scientometrics, Springer;Akadémiai Kiadó, vol. 105(1), pages 537-556, October.
    3. Marian-Gabriel Hâncean & Matjaž Perc & Lazăr Vlăsceanu, 2014. "Fragmented Romanian Sociology: Growth and Structure of the Collaboration Network," PLOS ONE, Public Library of Science, vol. 9(11), pages 1-9, November.
    4. Marian-Gabriel Hâncean & Matjaž Perc & Jürgen Lerner, 2021. "The coauthorship networks of the most productive European researchers," Scientometrics, Springer;Akadémiai Kiadó, vol. 126(1), pages 201-224, January.
    5. Duk Hee Lee & Il Won Seo & Ho Chull Choe & Hee Dae Kim, 2012. "Collaboration network patterns and research performance: the case of Korean public research institutions," Scientometrics, Springer;Akadémiai Kiadó, vol. 91(3), pages 925-942, June.
    6. Anzhi Sheng & Qi Su & Aming Li & Long Wang & Joshua B. Plotkin, 2023. "Constructing temporal networks with bursty activity patterns," Nature Communications, Nature, vol. 14(1), pages 1-10, December.
    7. Lemarchand, Guillermo A., 2012. "The long-term dynamics of co-authorship scientific networks: Iberoamerican countries (1973–2010)," Research Policy, Elsevier, vol. 41(2), pages 291-305.
    8. Ann Bostrom & Ragnar E. Löfstedt, 2003. "Communicating Risk: Wireless and Hardwired," Risk Analysis, John Wiley & Sons, vol. 23(2), pages 241-248, April.
    9. Pirvu Daniela & Barbuceanu Mircea, 2016. "Recent Contributions Of The Statistical Physics In The Research Of Banking, Stock Exchange And Foreign Exchange Markets," Annals - Economy Series, Constantin Brancusi University, Faculty of Economics, vol. 2, pages 85-92, April.
    10. Lilian Cervo Cabrera & Carlos Eduardo Caldarelli & Marcia Regina Gabardo Camara, 2020. "Mapping collaboration in international coffee certification research," Scientometrics, Springer;Akadémiai Kiadó, vol. 124(3), pages 2597-2618, September.
    11. De Montis, Andrea & Ganciu, Amedeo & Cabras, Matteo & Bardi, Antonietta & Mulas, Maurizio, 2019. "Comparative ecological network analysis: An application to Italy," Land Use Policy, Elsevier, vol. 81(C), pages 714-724.
    12. de Oliveira, Thaiane Moreira & de Albuquerque, Sofia & Toth, Janderson Pereira & Bello, Debora Zava, 2018. "International cooperation networks of the BRICS bloc," SocArXiv b6x43, Center for Open Science.
    13. Rosamaria d’Amore & Roberto Iorio & Agnieszka Stawinoga, 2011. "Who and where are the co-authors? The relationship between institutional and geographical distance in scientific publications," Working Papers 2011.4, International Network for Economic Research - INFER.
    14. Peng Liu & Haoxiang Xia, 2015. "Structure and evolution of co-authorship network in an interdisciplinary research field," Scientometrics, Springer;Akadémiai Kiadó, vol. 103(1), pages 101-134, April.
    15. Roth, Camille, 2007. "Empiricism for descriptive social network models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 378(1), pages 53-58.
    16. Elias Carroni & Paolo Pin & Simone Righi, 2020. "Bring a Friend! Privately or Publicly?," Management Science, INFORMS, vol. 66(5), pages 2269-2290, May.
    17. Jin, Jiashun & Ke, Zheng Tracy & Luo, Shengming, 2024. "Mixed membership estimation for social networks," Journal of Econometrics, Elsevier, vol. 239(2).
    18. Kim, Jinseok & Diesner, Jana, 2015. "The effect of data pre-processing on understanding the evolution of collaboration networks," Journal of Informetrics, Elsevier, vol. 9(1), pages 226-236.
    19. Shiau, Wen-Lung & Dwivedi, Yogesh K. & Yang, Han Suan, 2017. "Co-citation and cluster analyses of extant literature on social networks," International Journal of Information Management, Elsevier, vol. 37(5), pages 390-399.
    20. J. Sylvan Katz & Guillermo Armando Ronda-Pupo, 2019. "Cooperation, scale-invariance and complex innovation systems: a generalization," Scientometrics, Springer;Akadémiai Kiadó, vol. 121(2), pages 1045-1065, November.

    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:phsmap:v:556:y:2020:i:c:s0378437120303733. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.