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Growing networks with preferential addition and deletion of edgesPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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2009 (English)In: Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, E-ISSN 1873-2119, Vol. 388, no 19, p. 4297-4303Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

2009. Vol. 388, no 19, p. 4297-4303
##### Keywords [en]

Preferential attachment; Preferential deletion; Complex networks; Random graphs; Degree distribution
##### National Category

Mathematics
##### Identifiers

URN: urn:nbn:se:su:diva-36100DOI: 10.1016/j.physa.2009.06.032ISI: 000268653900034OAI: oai:DiVA.org:su-36100DiVA, id: diva2:288753
#####

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PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt572",{id:"formSmash:j_idt572",widgetVar:"widget_formSmash_j_idt572",multiple:true}); Available from: 2010-01-21 Created: 2010-01-21 Last updated: 2017-12-12Bibliographically approved

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 *π*_{1}>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 *π*_{2} 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 *π*_{3}=1−*π*_{1}−*π*_{2}<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 *p*_{k} of vertices with degree *k*, and solving this recursion reveals that, for *π*_{3}<1/3, we have *p*_{k}*k*^{−(3−7π3)/(1−3π3)}, while, for *π*_{3}>1/3, the fraction *p*_{k} decays exponentially at rate (*π*_{1}+*π*_{2})/2*π*_{3}. 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.

doi
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