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http://bura.brunel.ac.uk/handle/2438/8354
Title: | Kinetics of node splitting in evolving complex networks |
Authors: | Colman, ER Rodgers, GJ |
Keywords: | Random networks;Fragmentation;Scale-free networks;Disordered systems;Critical phenomena |
Issue Date: | 2012 |
Publisher: | Elsevier |
Citation: | Physica A: Statistical Mechanics and its Applications, 391(24), 6626 - 6631, Dec 2012 |
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. |
Description: | Copyright @ 2012 Elsevier B.V. All rights reserved. This is a preprint version of the published article which can be accessed at the link below. |
URI: | http://www.sciencedirect.com/science/article/pii/S0378437112007030 http://bura.brunel.ac.uk/handle/2438/8354 |
DOI: | http://dx.doi.org/10.1016/j.physa.2012.07.034 |
ISSN: | 0378-4371 |
Appears in Collections: | Publications Dept of Mathematics Research Papers Mathematical Sciences |
Files in This Item:
File | Description | Size | Format | |
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Preprint.pdf | 225.99 kB | Adobe PDF | View/Open |
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