Kinetics of node splitting in evolving complex networks |
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Authors: | E.R. Colman G.J. Rodgers |
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Affiliation: | Department of Mathematical Sciences, Brunel University, Uxbridge, Middlesex UB8 3PH, UK |
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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. |
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Keywords: | Random networks Fragmentation Scale-free networks Disordered systems Critical phenomena |
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