IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v353y2005icp661-673.html
   My bibliography  Save this article

On the formation of degree and cluster-degree correlations in scale-free networks

Author

Listed:
  • Yao, Xin
  • Zhang, Chang-shui
  • Chen, Jin-wen
  • Li, Yan-da

Abstract

The cluster-degree of a vertex is the number of connections among the neighbors of this vertex. In this paper we study the cluster-degree of the generalized Barabási–Albert model (GBA model) whose exponent of degree distribution ranges from 2 to ∞. We present the mean-field rate equation for clustering and obtain analytically the degree-dependence of the cluster-degree. We study the distribution of the cluster-degree, which is size dependent but the tail is kept invariant for different degree exponents in the GBA model. In addition, for the degree dependence of the clustering coefficient, very different behaviors arise for different cases of the GBA model. The physical sense of the invariance property of cluster-degree is explained and more general cases are discussed. All the above theoretical results are verified by simulation.

Suggested Citation

  • Yao, Xin & Zhang, Chang-shui & Chen, Jin-wen & Li, Yan-da, 2005. "On the formation of degree and cluster-degree correlations in scale-free networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 353(C), pages 661-673.
    • Handle: RePEc:eee:phsmap:v:353:y:2005:i:c:p:661-673
    DOI: 10.1016/j.physa.2005.01.036
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437105000683
    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.2005.01.036?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. Steven H. Strogatz, 2001. "Exploring complex networks," Nature, Nature, vol. 410(6825), pages 268-276, March.
    3. S. Redner, 1998. "How popular is your paper? An empirical study of the citation distribution," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 4(2), pages 131-134, July.
    4. Barabási, Albert-László & Albert, Réka & Jeong, Hawoong, 1999. "Mean-field theory for scale-free random networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 272(1), pages 173-187.
    5. Réka Albert & Hawoong Jeong & Albert-László Barabási, 1999. "Diameter of the World-Wide Web," Nature, Nature, vol. 401(6749), pages 130-131, September.
    6. H. Jeong & B. Tombor & R. Albert & Z. N. Oltvai & A.-L. Barabási, 2000. "The large-scale organization of metabolic networks," Nature, Nature, vol. 407(6804), pages 651-654, October.
    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. Tam, Wai M. & Lau, Francis C.M. & Tse, Chi K. & Xia, Yongxiang & Shan, Xiuming, 2006. "Effect of clustering in a complex user network on the telephone traffic," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 371(2), pages 745-753.

    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. Chen, Qinghua & Shi, Dinghua, 2006. "Markov chains theory for scale-free networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 360(1), pages 121-133.
    2. Laurienti, Paul J. & Joyce, Karen E. & Telesford, Qawi K. & Burdette, Jonathan H. & Hayasaka, Satoru, 2011. "Universal fractal scaling of self-organized networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(20), pages 3608-3613.
    3. Chen, Qinghua & Shi, Dinghua, 2004. "The modeling of scale-free networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 335(1), pages 240-248.
    4. Salcedo-Sanz, S. & Cuadra, L., 2019. "Quasi scale-free geographically embedded networks over DLA-generated aggregates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 1286-1305.
    5. Claes Andersson & Koen Frenken & Alexander Hellervik, 2006. "A Complex Network Approach to Urban Growth," Environment and Planning A, , vol. 38(10), pages 1941-1964, October.
    6. Wang, Huan & Xu, Chuan-Yun & Hu, Jing-Bo & Cao, Ke-Fei, 2014. "A complex network analysis of hypertension-related genes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 394(C), pages 166-176.
    7. J. Esquivel-Gómez & R. E. Balderas-Navarro & P. D. Arjona-Villicaña & P. Castillo-Castillo & O. Rico-Trejo & J. Acosta-Elias, 2017. "On the Emergence of Islands in Complex Networks," Complexity, Hindawi, vol. 2017, pages 1-10, January.
    8. 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.
    9. Rendón de la Torre, Stephanie & Kalda, Jaan & Kitt, Robert & Engelbrecht, Jüri, 2016. "On the topologic structure of economic complex networks: Empirical evidence from large scale payment network of Estonia," Chaos, Solitons & Fractals, Elsevier, vol. 90(C), pages 18-27.
    10. Fu, Jingcheng & Wu, Jianliang & Liu, Chuanjian & Xu, Jin, 2016. "Leaders in communities of real-world networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 428-441.
    11. Zheng, Xiaolong & Zeng, Daniel & Li, Huiqian & Wang, Feiyue, 2008. "Analyzing open-source software systems as complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(24), pages 6190-6200.
    12. Bryce Thomas & Raja Jurdak & Kun Zhao & Ian Atkinson, 2016. "Diffusion in Colocation Contact Networks: The Impact of Nodal Spatiotemporal Dynamics," PLOS ONE, Public Library of Science, vol. 11(8), pages 1-21, August.
    13. Matthew O. Jackson & Brian W. Rogers, 2005. "Search in the Formation of Large Networks: How Random are Socially Generated Networks?," Game Theory and Information 0503005, University Library of Munich, Germany.
    14. Paul Sheridan & Yuichi Yagahara & Hidetoshi Shimodaira, 2008. "A preferential attachment model with Poisson growth for scale-free networks," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 60(4), pages 747-761, December.
    15. Ikeda, N., 2007. "Network formed by traces of random walks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 379(2), pages 701-713.
    16. Roland Pongou & Guy Tchuente & Jean-Baptiste Tondji, 2021. "Optimally Targeting Interventions in Networks during a Pandemic: Theory and Evidence from the Networks of Nursing Homes in the United States," Papers 2110.10230, arXiv.org.
    17. Laurie A. Schintler & Aura Reggiani & Rajendra Kulkarni & Peter Nijkamp, 2003. "Scale-Free Phenomena in Communication Networks: A Cross-Atlantic Comparison," ERSA conference papers ersa03p436, European Regional Science Association.
    18. Yang, Yang & Sun, Peng Gang & Hu, Xia & Li, Zhou Jun, 2014. "Closed walks for community detection," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 397(C), pages 129-143.
    19. Tsonis, A.A. & Roebber, P.J., 2004. "The architecture of the climate network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 333(C), pages 497-504.
    20. Colman, E.R. & Rodgers, G.J., 2013. "Complex scale-free networks with tunable power-law exponent and clustering," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(21), pages 5501-5510.

    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:353:y:2005:i:c:p:661-673. 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.