Kinetics of node splitting in evolving complex networks
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.
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Volume (Year): 391 (2012)
Issue (Month): 24 ()
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- S. Redner, 1998. "How popular is your paper? An empirical study of the citation distribution," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 4(2), pages 131-134, July.
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