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Growing networks with preferential addition and deletion of edges
Stockholm University, Faculty of Science, Department of Mathematics.
Stockholm University, Faculty of Science, Department of Mathematics.
2009 (English)In: Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, E-ISSN 1873-2119, Vol. 388, no 19, 4297-4303 p.Article in journal (Refereed) Published
##### Abstract [en]

A preferential attachment model for a growing network incorporating the deletion of edges is studied and the expected asymptotic degree distribution is analyzed. At each time step t=1,2,…, with probability π1>0 a new vertex with one edge attached to it is added to the network and the edge is connected to an existing vertex chosen proportionally to its degree, with probability π2 a vertex is chosen proportionally to its degree and an edge is added between this vertex and a randomly chosen other vertex, and with probability π3=1−π1π2<1/2 a vertex is chosen proportionally to its degree and a random edge of this vertex is deleted. The model is intended to capture a situation where high-degree vertices are more dynamic than low-degree vertices in the sense that their connections tend to be changing. A recursion formula is derived for the expected asymptotic fraction pk of vertices with degree k, and solving this recursion reveals that, for π3<1/3, we have pkk−(3−7π3)/(1−3π3), while, for π3>1/3, the fraction pk decays exponentially at rate (π1+π2)/2π3. There is hence a non-trivial upper bound for how much deletion the network can incorporate without losing the power-law behavior of the degree distribution. The analytical results are supported by simulations.

##### Place, publisher, year, edition, pages
2009. Vol. 388, no 19, 4297-4303 p.
##### Keyword [en]
Preferential attachment; Preferential deletion; Complex networks; Random graphs; Degree distribution
Mathematics
##### Identifiers
ISI: 000268653900034OAI: oai:DiVA.org:su-36100DiVA: diva2:288753
Available from: 2010-01-21 Created: 2010-01-21 Last updated: 2017-12-12Bibliographically approved

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Physica A: Statistical Mechanics and its Applications
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