Kinetics of node splitting in evolving complex networks

E.R. Colman and G.J. Rodgers

Physica A: Statistical Mechanics and its Applications, 2012, vol. 391, issue 24, 6626-6631

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.

Keywords: Random networks; Fragmentation; Scale-free networks; Disordered systems; Critical phenomena (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:391:y:2012:i:24:p:6626-6631

DOI: 10.1016/j.physa.2012.07.034

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