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Topology of growing networks accelerated by intermediary process

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  • Ikeda, Nobutoshi

Abstract

We examined the effect of accelerated growth (increase in the mean vertex degree) caused by internal links between pre-existing nodes on the topology of growing networks and showed that a kind of local rule, edge additions stimulated by randomly chosen intermediaries (intermediary process), not only guarantees a highly clustered structure but also induces the scale-free property on growing networks without an explicit preferential rule with the aid of accelerating growth. We relate the power-law exponent γ describing the degree distribution to the rate of acceleration and an internal factor which expresses the contribution of internal links to the rate of increase in degrees. The behavior of the internal factor generates different forms of time dependence of degrees according to whether γ>2 or γ<2. Accelerating growth plays a dominant role in the structural formation of networks based on local rules, in contrast to cases when non-local rules are applied, because similar studies showed that a simple preferential linking rule (a non-local rule) easily induces power laws without accelerating growth.

Suggested Citation

  • Ikeda, Nobutoshi, 2017. "Topology of growing networks accelerated by intermediary process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 484(C), pages 378-393.
    • Handle: RePEc:eee:phsmap:v:484:y:2017:i:c:p:378-393
    DOI: 10.1016/j.physa.2017.04.123
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    References listed on IDEAS

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    1. Sen, Parongama, 2005. "Directed accelerated growth: application in citation network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 346(1), pages 139-146.
    2. Ikeda, Nobutoshi, 2015. "Effects of triad formations stimulated by intermediaries on network topology," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 436(C), pages 897-908.
    3. Barabási, A.L & Jeong, H & Néda, Z & Ravasz, E & Schubert, A & Vicsek, T, 2002. "Evolution of the social network of scientific collaborations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 311(3), pages 590-614.
    4. Zhang, Zhongzhi & Fang, Lujun & Zhou, Shuigeng & Guan, Jihong, 2009. "Effects of accelerating growth on the evolution of weighted complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(2), pages 225-232.
    5. Ikeda, Nobutoshi, 2010. "Impact of initial lattice structures on networks generated by traces of random walks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(16), pages 3336-3347.
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    1. Ikeda, Nobutoshi, 2021. "Stratified structure of fractal scale-free networks generated by local rules," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 583(C).
    2. Ikeda, Nobutoshi, 2019. "Growth model for fractal scale-free networks generated by a random walk," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 424-434.
    3. Sheida Hasani & Razieh Masoomi & Jamshid Ardalankia & Mohammadbashir Sedighi & Hamid Jafari, 2019. "Growth Dynamics of Value and Cost Trade-off in Temporal Networks," Papers 1908.11433, arXiv.org, revised Aug 2020.

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