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Fractional Dynamics of Network Growth Constrained by Aging Node Interactions

Author

Listed:
  • Hadiseh Safdari
  • Milad Zare Kamali
  • Amirhossein Shirazi
  • Moein Khalighi
  • Gholamreza Jafari
  • Marcel Ausloos

Abstract

In many social complex systems, in which agents are linked by non-linear interactions, the history of events strongly influences the whole network dynamics. However, a class of “commonly accepted beliefs” seems rarely studied. In this paper, we examine how the growth process of a (social) network is influenced by past circumstances. In order to tackle this cause, we simply modify the well known preferential attachment mechanism by imposing a time dependent kernel function in the network evolution equation. This approach leads to a fractional order Barabási-Albert (BA) differential equation, generalizing the BA model. Our results show that, with passing time, an aging process is observed for the network dynamics. The aging process leads to a decay for the node degree values, thereby creating an opposing process to the preferential attachment mechanism. On one hand, based on the preferential attachment mechanism, nodes with a high degree are more likely to absorb links; but, on the other hand, a node’s age has a reduced chance for new connections. This competitive scenario allows an increased chance for younger members to become a hub. Simulations of such a network growth with aging constraint confirm the results found from solving the fractional BA equation. We also report, as an exemplary application, an investigation of the collaboration network between Hollywood movie actors. It is undubiously shown that a decay in the dynamics of their collaboration rate is found, even including a sex difference. Such findings suggest a widely universal application of the so generalized BA model.

Suggested Citation

  • Hadiseh Safdari & Milad Zare Kamali & Amirhossein Shirazi & Moein Khalighi & Gholamreza Jafari & Marcel Ausloos, 2016. "Fractional Dynamics of Network Growth Constrained by Aging Node Interactions," PLOS ONE, Public Library of Science, vol. 11(5), pages 1-13, May.
  • Handle: RePEc:plo:pone00:0154983
    DOI: 10.1371/journal.pone.0154983
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    Cited by:

    1. 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.
    2. Ghosh, Uttam & Pal, Swadesh & Banerjee, Malay, 2021. "Memory effect on Bazykin’s prey-predator model: Stability and bifurcation analysis," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    3. Rabbani, Fereshteh & Khraisha, Tamer & Abbasi, Fatemeh & Jafari, Gholam Reza, 2021. "Memory effects on link formation in temporal networks: A fractional calculus approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 564(C).
    4. Jamshid Ardalankia & Jafar Askari & Somaye Sheykhali & Emmanuel Haven & G. Reza Jafari, 2020. "Mapping Coupled Time-series Onto Complex Network," Papers 2004.13536, arXiv.org, revised Aug 2020.
    5. Majumdar, Prahlad & Mondal, Bapin & Debnath, Surajit & Ghosh, Uttam, 2022. "Controlling of periodicity and chaos in a three dimensional prey predator model introducing the memory effect," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).

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