CiteExport$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_upper_j_idt156",{id:"formSmash:upper:j_idt156",widgetVar:"widget_formSmash_upper_j_idt156",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:upper:exportLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_upper_j_idt157_j_idt159",{id:"formSmash:upper:j_idt157:j_idt159",widgetVar:"widget_formSmash_upper_j_idt157_j_idt159",target:"formSmash:upper:j_idt157:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});

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});
function selectAll()
{
var panelSome = $(PrimeFaces.escapeClientId("formSmash:some"));
var panelAll = $(PrimeFaces.escapeClientId("formSmash:all"));
panelAll.toggle();
toggleList(panelSome.get(0).childNodes, panelAll);
toggleList(panelAll.get(0).childNodes, panelAll);
}
/*Toggling the list of authorPanel nodes according to the toggling of the closeable second panel */
function toggleList(childList, panel)
{
var panelWasOpen = (panel.get(0).style.display == 'none');
// console.log('panel was open ' + panelWasOpen);
for (var c = 0; c < childList.length; c++) {
if (childList[c].classList.contains('authorPanel')) {
clickNode(panelWasOpen, childList[c]);
}
}
}
/*nodes have styleClass ui-corner-top if they are expanded and ui-corner-all if they are collapsed */
function clickNode(collapse, child)
{
if (collapse && child.classList.contains('ui-corner-top')) {
// console.log('collapse');
child.click();
}
if (!collapse && child.classList.contains('ui-corner-all')) {
// console.log('expand');
child.click();
}
}
PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 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]

##### 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
##### National Category

Mathematics
##### Identifiers

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

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt449",{id:"formSmash:j_idt449",widgetVar:"widget_formSmash_j_idt449",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt456",{id:"formSmash:j_idt456",widgetVar:"widget_formSmash_j_idt456",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt462",{id:"formSmash:j_idt462",widgetVar:"widget_formSmash_j_idt462",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
urn-nbn$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_j_idt1166",{id:"formSmash:j_idt1166",widgetVar:"widget_formSmash_j_idt1166",showEffect:"fade",hideEffect:"fade",showDelay:500,hideDelay:300,target:"formSmash:altmetricDiv"});});

CiteExport$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_lower_j_idt1219",{id:"formSmash:lower:j_idt1219",widgetVar:"widget_formSmash_lower_j_idt1219",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:lower:exportLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_lower_j_idt1220_j_idt1222",{id:"formSmash:lower:j_idt1220:j_idt1222",widgetVar:"widget_formSmash_lower_j_idt1220_j_idt1222",target:"formSmash:lower:j_idt1220:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});