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Kinetics of node splitting in evolving complex networks

Author

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  • Colman, E.R.
  • Rodgers, G.J.

Abstract

We introduce a collection of complex networks generated by a combination of preferential attachment and a previously unexamined process of “splitting” nodes of degree k into k nodes of degree 1. Four networks are considered, each evolves at each time step by either preferential attachment, with probability p, or splitting with probability 1−p. Two methods of attachment are considered; first, attachment of an edge between a newly created node and an existing node in the network, and secondly by attachment of an edge between two existing nodes. Splitting is also considered in two separate ways; first by selecting each node with equal probability and secondly, selecting the node with probability proportional to its degree. Exact solutions for the degree distributions are found and scale-free structure is exhibited in those networks where the candidates for splitting are chosen with uniform probability, those that are chosen preferentially are distributed with a power law with exponential cut-off.

Suggested Citation

  • Colman, E.R. & Rodgers, G.J., 2012. "Kinetics of node splitting in evolving complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(24), pages 6626-6631.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:24:p:6626-6631
    DOI: 10.1016/j.physa.2012.07.034
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    References listed on IDEAS

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    3. R. D'Hulst & G. J. Rodgers, 2000. "Exact Solution Of A Model For Crowding And Information Transmission In Financial Markets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 3(04), pages 609-616.
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