Probabilistic prediction in scale-free networksDiameter changes

《Probabilistic prediction in scale-free networksDiameter changes》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

1、[Phys.Rev.Lett.91,058701(2003)]Probabilisticpredictioninscale-freenetworks:DiameterchangesJ.-H.Kim,K.-I.Goh,B.KahngandD.KimSchoolofPhysicsandCenterforTheoreticalPhysics,SeoulNationalUniversity,Seoul151-747,Korea(Dated:February1,2008)Incomplexsystems,responsestos

2、mallperturbationsaretoodiversetopredicthowmuchtheywouldbedefinitely,andthensuchdiverseresponsescanbepredictedinaprobabilisticway.Herewestudysuchaprobleminscale-freenetworks,forexample,thediameterchangesbythedeletionofasinglevertexforvariousinsilicoandrealworldsca

3、le-freenetworks.Wefindthatthediameterchangesareindeeddiverseandtheirdistributionexhibitsanalgebraicdecaywithanexponentzasymptotically.Interestingly,theexponentzisrobustasz≃2.2(1)formostscale-freenetworks,insensitivetothedegreeexponentsgaslongas2

4、isanothertypewithz≃1.7(1)anditsexamplesincludetheInternetanditsrelatedinsilicomodel.PACSnumbers:89.70.+c,89.75.-k,05.10.-aAcomplexsystemconsistsofmanyconstituents,generat-perturbationsandcheckiftheconceptofprobabilisticpre-ingemergingbehaviorsthroughdiverseinter

5、actions[1,2].dictioncanbeapplied.Forthispurpose,weinvestigateaOneofthepowerfulwaysofexaminingtheintrinsicnaturesimpleproblemofdiameterchangewhenasinglevertexisofacomplexsystemistoobservehowsuchemergingpat-removedfromthesystem.Diameter,definedastheaverageternschan

6、gebysmallperturbationappliedtothesystem.Indistancebetweeneverypairofverticesinanetwork,isasim-complexsystems,suchachangeorresponseissosensitivepleyetfundamentalquantityofSFnetworkstocharacterizetothedetailsoftheperturbationthatitisextremelydiverse.thesmall-world

7、nature,andcanbethoughtofasameasureInsuchacase,itisnotadequatetopredicthowmuchthereflectingtheefficiencyofanetwork.Ourmaininterestischangewouldbedefinitely.Recently,Parisihasargued[3]howmuchtheefficiencyofanetworkwouldbeaffectedbythatthepredictionfortheresponsestosma

8、llperturbationstheremovalofasinglevertex.Whenavertexisremoved,incomplexsystemscanbemadeinaprobabilisticway.Heeachpairofremainingverticeswhoseshortestpathwayhadshowede