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1、REVIEWSComplexbrainnetworks:graphtheoreticalanalysisofstructuralandfunctionalsystemsEdBullmore*‡andOlafSporns§Abstract
2、Recentdevelopmentsinthequantitativeanalysisofcomplexnetworks,basedlargelyongraphtheory,havebeenrapidlytranslatedtostudiesofbrainnetwor
3、korganization.Thebrain’sstructuralandfunctionalsystemshavefeaturesofcomplexnetworks—suchassmall-worldtopology,highlyconnectedhubsandmodularity—bothatthewhole-brainscaleofhumanneuroimagingandatacellularscaleinnon-humananimals.Inthisarticle,wereviewstudie
4、sinvestigatingcomplexbrainnetworksindiverseexperimentalmodalities(includingstructuralandfunctionalMRI,diffusiontensorimaging,magnetoencephalogra-phyandelectroencephalographyinhumans)andprovideanaccessibleintroductiontothebasicprinciplesofgraphtheory.Wea
5、lsohighlightsomeofthetechnicalchallengesandkeyquestionstobeaddressedbyfuturedevelopmentsinthisrapidlymovingfield.Wehaveknownsincethenineteenthcenturythatthehasledtoafundamentalinsight:substantivelydifferentGraphtheoryneuronalelementsofthebrainconstitute
6、aformidablycomplexsystemsoftensharecertainkeyorganizationalAbranchofmathematicsthatcomplicatedstructuralnetwork1,2.Sincethetwentiethprinciples,andthesecanbequantitativelycharacterizeddealswiththeformaldescriptionandanalysisofcenturyithasalsobeenwidelyap
7、preciatedthatthisbythesameparameters(BOX2).Inotherwords,manygraphs.Agraphisdefinedanatomicalsubstratesupportsthedynamicemergencecomplexsystemsshowremarkablysimilarmacroscopicsimplyasasetofnodesofcoherentphysiologicalactivity,suchasphase-lockedbehaviourd
8、espiteprofounddifferencesinthemicro-(vertices)linkedbyconnections(edges),andmaybedirectedhigh-frequencyelectromagneticoscillations,thatcanscopicdetailsoftheelementsofeachsystemortheirorundirected.Whendescribingspanthemultiplespatiallydistinctbrainregion
9、sthatmechanismsofinteraction.areal-worldsystem,agraphmakeupafunctionalnetwork3,4.SuchnetworksareOneexampleofanapparentlyubiquitousmacro-providesanabstractthoughttoprovidethephysiologicalbasisforinforma-scopicbehaviourincomplexsys
