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Random networks are heterogeneous exhibiting a multi-scaling law

Author

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  • Sun, Peng Gang
  • Che, Wanping
  • Quan, Yining
  • Wang, Shuzhen
  • Miao, Qiguang

Abstract

Unlike the scale-free (SF) architecture, random networks of the Erdos–Renyi (ER) are also called homogeneous networks consisting of the same kind of nodes because these nodes approximately have same degrees, which follow a Poisson distribution. This paper tries to demonstrate that this random network is actually heterogeneous, i.e., it is composed of different kinds of nodes by introducing a new metric, called B-index to quantify a node, defined as the extent that the node’s removal can break down its neighborhood. One interesting phenomenon is observed on random networks, i.e., the distribution of B-index can be roughly divided into many sub-distributions with different scalings exhibiting a multi-scaling law. This phenomenon appears, fluctuates and disappears as the changes of random networks. In addition, the analysis of spreading dynamics on the susceptible infected recovered (SIR) model suggests that the nodes with the highest B-index can alleviate the overlap problem of infected area of multiple origins, and are more influential for the spreading of epidemics, especially for the small number of origins.

Suggested Citation

  • Sun, Peng Gang & Che, Wanping & Quan, Yining & Wang, Shuzhen & Miao, Qiguang, 2022. "Random networks are heterogeneous exhibiting a multi-scaling law," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 587(C).
    • Handle: RePEc:eee:phsmap:v:587:y:2022:i:c:s0378437121007524
    DOI: 10.1016/j.physa.2021.126479
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    References listed on IDEAS

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    1. Steven H. Strogatz, 2001. "Exploring complex networks," Nature, Nature, vol. 410(6825), pages 268-276, March.
    2. Yang, Shi-Jie & Zhao, Hu, 2006. "Generating multi-scaling networks with two types of vertices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(2), pages 863-868.
    3. Flaviano Morone & Hernán A. Makse, 2015. "Correction: Corrigendum: Influence maximization in complex networks through optimal percolation," Nature, Nature, vol. 527(7579), pages 544-544, November.
    4. Yanqing Hu & Shenggong Ji & Yuliang Jin & Ling Feng & H. Eugene Stanley & Shlomo Havlin, 2018. "Local structure can identify and quantify influential global spreaders in large scale social networks," Proceedings of the National Academy of Sciences, Proceedings of the National Academy of Sciences, vol. 115(29), pages 7468-7472, July.
    5. Tibor Braun & Wolfgang Glänzel & András Schubert, 2006. "A Hirsch-type index for journals," Scientometrics, Springer;Akadémiai Kiadó, vol. 69(1), pages 169-173, October.
    6. Pablo M. Gleiser & Leon Danon, 2003. "Community Structure In Jazz," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 6(04), pages 565-573.
    7. Doina Bucur & Petter Holme, 2020. "Beyond ranking nodes: Predicting epidemic outbreak sizes by network centralities," PLOS Computational Biology, Public Library of Science, vol. 16(7), pages 1-20, July.
    8. Réka Albert & Hawoong Jeong & Albert-László Barabási, 2000. "Error and attack tolerance of complex networks," Nature, Nature, vol. 406(6794), pages 378-382, July.
    9. Flaviano Morone & Hernán A. Makse, 2015. "Influence maximization in complex networks through optimal percolation," Nature, Nature, vol. 524(7563), pages 65-68, August.
    10. Linyuan Lü & Tao Zhou & Qian-Ming Zhang & H. Eugene Stanley, 2016. "The H-index of a network node and its relation to degree and coreness," Nature Communications, Nature, vol. 7(1), pages 1-7, April.
    Full references (including those not matched with items on IDEAS)

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