IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v388y2009i14p2941-2948.html
   My bibliography  Save this article

Local affinity in heterogeneous growing networks

Author

Listed:
  • Santiago, A.
  • Benito, R.M.

Abstract

In this paper we present a study of the influence of local affinity in heterogeneous preferential attachment (PA) networks. Heterogeneous PA models are a generalization of the Barabási–Albert model to heterogeneous networks, where the affinity between nodes biases the attachment probability of links. Threshold models are a class of heterogeneous PA models where the affinity between nodes is inversely related to the distance between their states. We propose a generalization of threshold models where network nodes have individual affinity functions, which are then combined to yield the affinity of each potential interaction. We analyze the influence of the affinity functions in the topological properties averaged over a network ensemble. The network topology is evaluated through the distributions of connectivity degrees, clustering coefficients and geodesic distances. We show that the relaxation of the criterion of a single global affinity still leads to a reasonable power-law scaling in the connectivity and clustering distributions under a wide spectrum of assumptions. We also show that the richer behavior of the model often exhibits a better agreement with the empirical observations on real networks.

Suggested Citation

  • Santiago, A. & Benito, R.M., 2009. "Local affinity in heterogeneous growing networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(14), pages 2941-2948.
  • Handle: RePEc:eee:phsmap:v:388:y:2009:i:14:p:2941-2948
    DOI: 10.1016/j.physa.2009.03.039
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437109002179
    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.2009.03.039?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. A. Santiago & R. M. Benito, 2007. "Emergence Of Multiscaling In Heterogeneous Complex Networks," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 18(10), pages 1591-1607.
    2. Ergün, G. & Rodgers, G.J., 2002. "Growing random networks with fitness," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 303(1), pages 261-272.
    3. 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.
    4. Steven H. Strogatz, 2001. "Exploring complex networks," Nature, Nature, vol. 410(6825), pages 268-276, March.
    5. Barthélemy, Marc & Barrat, Alain & Pastor-Satorras, Romualdo & Vespignani, Alessandro, 2005. "Characterization and modeling of weighted networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 346(1), pages 34-43.
    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. Santiago, A. & Benito, R.M., 2008. "Connectivity degrees in the threshold preferential attachment model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(10), pages 2365-2376.
    2. Santiago, A. & Benito, R.M., 2009. "Robustness of heterogeneous complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(11), pages 2234-2242.
    3. Colizza, Vittoria & Flammini, Alessandro & Maritan, Amos & Vespignani, Alessandro, 2005. "Characterization and modeling of protein–protein interaction networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 352(1), pages 1-27.
    4. Li, Chunguang & Chen, Guanrong, 2004. "Synchronization in general complex dynamical networks with coupling delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 343(C), pages 263-278.
    5. 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.
    6. L. Jarina Banu & P. Balasubramaniam, 2014. "Synchronisation of discrete-time complex networks with randomly occurring uncertainties, nonlinearities and time-delays," International Journal of Systems Science, Taylor & Francis Journals, vol. 45(7), pages 1427-1450, July.
    7. 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.
    8. Liu, Z.X. & Chen, Z.Q. & Yuan, Z.Z., 2007. "Pinning control of weighted general complex dynamical networks with time delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 375(1), pages 345-354.
    9. Wen, Guanghui & Duan, Zhisheng & Chen, Guanrong & Geng, Xianmin, 2011. "A weighted local-world evolving network model with aging nodes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(21), pages 4012-4026.
    10. Ruskin, Heather J. & Burns, John, 2006. "Weighted networks in immune system shape space," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 365(2), pages 549-555.
    11. Daniel Straulino & Mattie Landman & Neave O'Clery, 2020. "A bi-directional approach to comparing the modular structure of networks," Papers 2010.06568, arXiv.org.
    12. Kii, Masanobu & Akimoto, Keigo & Doi, Kenji, 2012. "Random-growth urban model with geographical fitness," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(23), pages 5960-5970.
    13. Reppas, Andreas I. & Spiliotis, Konstantinos & Siettos, Constantinos I., 2015. "Tuning the average path length of complex networks and its influence to the emergent dynamics of the majority-rule model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 109(C), pages 186-196.
    14. Chen, Qinghua & Chen, Shenghui, 2007. "A highly clustered scale-free network evolved by random walking," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 383(2), pages 773-781.
    15. 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.
    16. Ying Duan & Xiuwen Fu & Wenfeng Li & Yu Zhang & Giancarlo Fortino, 2017. "Evolution of Scale-Free Wireless Sensor Networks with Feature of Small-World Networks," Complexity, Hindawi, vol. 2017, pages 1-15, July.
    17. 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.
    18. Milena Oehlers & Benjamin Fabian, 2021. "Graph Metrics for Network Robustness—A Survey," Mathematics, MDPI, vol. 9(8), pages 1-48, April.
    19. Ni, Shunjiang & Weng, Wenguo & Zhang, Hui, 2011. "Modeling the effects of social impact on epidemic spreading in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4528-4534.
    20. Ikeda, N., 2007. "Network formed by traces of random walks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 379(2), pages 701-713.

    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:388:y:2009:i:14:p:2941-2948. 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.