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On the distributions of Laplacian eigenvalues versus node degrees in complex networks

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  • Zhan, Choujun
  • Chen, Guanrong
  • Yeung, Lam F.

Abstract

In this paper, the important issue of Laplacian eigenvalue distributions is investigated through theory-guided extensive numerical simulations, for four typical complex network models, namely, the ER random-graph networks, WS and NW small-world networks, and BA scale-free networks. It is found that these four types of complex networks share some common features, particularly similarities between the Laplacian eigenvalue distributions and the node degree distributions.

Suggested Citation

  • Zhan, Choujun & Chen, Guanrong & Yeung, Lam F., 2010. "On the distributions of Laplacian eigenvalues versus node degrees in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(8), pages 1779-1788.
    • Handle: RePEc:eee:phsmap:v:389:y:2010:i:8:p:1779-1788
    DOI: 10.1016/j.physa.2009.12.005
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    References listed on IDEAS

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    1. Jalan, Sarika & Bandyopadhyay, Jayendra N., 2008. "Random matrix analysis of network Laplacians," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(2), pages 667-674.
    2. Steven H. Strogatz, 2001. "Exploring complex networks," Nature, Nature, vol. 410(6825), pages 268-276, March.
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    Cited by:

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    2. Liu, Yang & Ouyang, Jinzhi & Zhao, Ronghui & Shi, Haobin & Pan, Wei & Ma, Fei, 2025. "Structural transition on partial edge-based growing graph," Chaos, Solitons & Fractals, Elsevier, vol. 201(P2).
    3. Ma, Tinghuai & Li, Lu & Ji, Sai & Wang, Xin & Tian, Yuan & Al-Dhelaan, Abdullah & Al-Rodhaan, Mznah, 2014. "Optimized Laplacian image sharpening algorithm based on graphic processing unit," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 416(C), pages 400-410.
    4. Deyasi, Krishanu & Chakraborty, Abhijit & Banerjee, Anirban, 2017. "Network similarity and statistical analysis of earthquake seismic data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 481(C), pages 224-234.
    5. Bayani, Atiyeh & Alexander, Prasina & Azarnoush, Hamed & Rajagopal, Karthikeyan & Jafari, Sajad & Nazarimehr, Fahimeh, 2023. "Designing networks with specific synchronization transitions independent of the system’s dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 632(P1).
    6. repec:plo:pone00:0037911 is not listed on IDEAS

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