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Dynamics of directed graphs: the world-wide Web

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  • Tadić, Bosiljka

Abstract

We introduce and simulate a growth model of the world-wide Web based on the dynamics of outgoing links that is motivated by the conduct of the agents in the real Web to update outgoing links (re)directing them towards constantly changing selected nodes. Emergent statistical correlation between the distributions of outgoing and incoming links is a key feature of the dynamics of the Web. The growth phase is characterized by temporal fractal structures which are manifested in the hierarchical organization of links. We obtain quantitative agreement with the recent empirical data in the real Web for the distributions of in- and out-links and for the size of the connected component. In a fully grown network of N nodes, we study the structure of connected clusters of nodes that are accessible along outgoing links from a randomly selected node. The distributions of size and depth of the connected clusters with a giant component exhibit supercritical behavior. By decreasing the control parameter – average fraction β of updated and added links per time step – towards βc(N)<10% the Web can resume a critical structure with no giant component in it. We find a different universality class when the updates of links are not allowed, i.e., for β≡0, corresponding to the network of science citations.

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  • Tadić, Bosiljka, 2001. "Dynamics of directed graphs: the world-wide Web," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 293(1), pages 273-284.
    • Handle: RePEc:eee:phsmap:v:293:y:2001:i:1:p:273-284
    DOI: 10.1016/S0378-4371(01)00014-0
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    References listed on IDEAS

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    1. Dhar, Deepak, 1999. "The Abelian sandpile and related models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 263(1), pages 4-25.
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    Cited by:

    1. Xiang, L.Y. & Liu, Z.X. & Chen, Z.Q. & Chen, F. & Yuan, Z.Z., 2007. "Pinning control of complex dynamical networks with general topology," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 379(1), pages 298-306.
    2. Lin, Yi & Zhang, Jianwei & Yang, Bo & Liu, Hong & Zhao, Liping, 2019. "An optimal routing strategy for transport networks with minimal transmission cost and high network capacity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 551-561.
    3. Andjelković, Miroslav & Tadić, Bosiljka & Maletić, Slobodan & Rajković, Milan, 2015. "Hierarchical sequencing of online social graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 436(C), pages 582-595.
    4. Derrible, Sybil & Kennedy, Christopher, 2010. "The complexity and robustness of metro networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(17), pages 3678-3691.
    5. Ouyang, Min & Yu, Ming-Hui & Huang, Xiang-Zhao & Luan, En-Jie, 2008. "Emergency response to disaster-struck scale-free network with redundant systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(18), pages 4683-4691.
    6. 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.

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