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Detection of topological patterns in complex networks: correlation profile of the internet

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  • Maslov, Sergei
  • Sneppen, Kim
  • Zaliznyak, Alexei

Abstract

A general scheme for detecting and analyzing topological patterns in large complex networks is presented. In this scheme the network in question is compared with its properly randomized version that preserves some of its low-level topological properties. Statistically significant deviation of any topological property of a network from this null model likely reflects its design principles and/or evolutionary history. We illustrate this basic scheme using the example of the correlation profile of the Internet quantifying correlations between degrees of its neighboring nodes. This profile distinguishes the Internet from previously studied molecular networks with a similar scale-free degree distribution. We finally demonstrate that the clustering in a network is very sensitive to both the degree distribution and its correlation profile and compare the clustering in the Internet to the appropriate null model.

Suggested Citation

  • Maslov, Sergei & Sneppen, Kim & Zaliznyak, Alexei, 2004. "Detection of topological patterns in complex networks: correlation profile of the internet," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 333(C), pages 529-540.
    • Handle: RePEc:eee:phsmap:v:333:y:2004:i:c:p:529-540
    DOI: 10.1016/j.physa.2003.06.002
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    Cited by:

    1. Bokwon Lee & Kyu-Min Lee & Jae-Suk Yang, 2019. "Network structure reveals patterns of legal complexity in human society: The case of the Constitutional legal network," PLOS ONE, Public Library of Science, vol. 14(1), pages 1-15, January.
    2. Christoph Schmidt & Thomas Weiss & Thomas Lehmann & Herbert Witte & Lutz Leistritz, 2013. "Extracting Labeled Topological Patterns from Samples of Networks," PLOS ONE, Public Library of Science, vol. 8(8), pages 1-11, August.
    3. Wen, Shaobo & An, Haizhong & Chen, Zhihua & Liu, Xueyong, 2017. "Driving factors of interactions between the exchange rate market and the commodity market: A wavelet-based complex network perspective," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 479(C), pages 299-308.
    4. Stephan Bialonski & Martin Wendler & Klaus Lehnertz, 2011. "Unraveling Spurious Properties of Interaction Networks with Tailored Random Networks," PLOS ONE, Public Library of Science, vol. 6(8), pages 1-13, August.
    5. Yourui Huang & Zhenping Chen & Tao Han & Xiaotao Liu, 2018. "One energy-efficient random-walk topology evolution method for underground wireless sensor networks," International Journal of Distributed Sensor Networks, , vol. 14(9), pages 15501477188, September.
    6. Nian, Fuzhong & Liu, Weilong, 2016. "Hybrid synchronization of heterogeneous chaotic systems on dynamic network," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 554-561.
    7. Sun, Ling & Liu, Yun & Bartolacci, Michael R. & Ting, I-Hsien, 2016. "A multi information dissemination model considering the interference of derivative information," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 451(C), pages 541-548.
    8. Huang, Xuan & An, Haizhong & Gao, Xiangyun & Hao, Xiaoqing & Liu, Pengpeng, 2015. "Multiresolution transmission of the correlation modes between bivariate time series based on complex network theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 428(C), pages 493-506.
    9. Liming Zhang & Ming Cai & Yingxin Zhang & Shuai Wang & Yao Xiao, 2024. "Two-layer network evolutionary game model applied to complex systems," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 97(11), pages 1-17, November.
    10. Pigorsch, U. & Sabek, M., 2022. "Assortative mixing in weighted directed networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 604(C).
    11. Wang, Fei & Yang, Yongqing, 2018. "Quasi-synchronization for fractional-order delayed dynamical networks with heterogeneous nodes," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 1-14.
    12. Giorgio Fagiolo & Tiziano Squartini & Diego Garlaschelli, 2013. "Null models of economic networks: the case of the world trade web," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 8(1), pages 75-107, April.
    13. Luu, Duc Thi & Lux, Thomas & Yanovski, Boyan, 2017. "Structural correlations in the Italian overnight money market: An analysis based on network configuration models," Economics Working Papers 2017-02, Christian-Albrechts-University of Kiel, Department of Economics.
    14. Xiao, Yu & Han, Jingti, 2016. "Forecasting new product diffusion with agent-based models," Technological Forecasting and Social Change, Elsevier, vol. 105(C), pages 167-178.
    15. Luo, Xiaojuan & Hu, Yuhen & Zhu, Yu, 2014. "Topology evolution model for wireless multi-hop network based on socially inspired mechanism," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 416(C), pages 639-650.
    16. Dhal, R. & Abad Torres, J. & Roy, S., 2015. "Detecting link failures in complex network processes using remote monitoring," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 437(C), pages 36-54.
    17. Yin, Liang & Shi, Li-Chen & Zhao, Jun-Yan & Du, Song-Yang & Xie, Wen-Bo & Yuan, Fei & Chen, Duan-Bing, 2018. "Heterogeneous information network model for equipment-standard system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 935-943.
    18. Zhang, Zhiwei & Wang, Zhenyu, 2017. "The data-driven null models for information dissemination tree in social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 484(C), pages 394-411.
    19. Wen, Xing-Zhang & Zheng, Yue & Du, Wen-Li & Ren, Zhuo-Ming, 2023. "Regulating clustering and assortativity affects node centrality in complex networks," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).

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