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1、AnInvestigationofSynchronyinTransportNetworksREXK.KINCAID1,NATALIAALEXANDROV2,ANDMICHAELJ.HOLROYD31DepartmentofMathematics,TheCollegeofWilliamandMary,Williamsburg,Virginia;2NASALangleyResearchCenter,Hampton,Virginia;and3DepartmentofComputerScience,UniversityofVirginia,Charlottesville,Vi
2、rginiaReceivedFebruary27,2007;acceptedMay23,2008Thecumulativedegreedistributionsoftransportnetworks,suchasairtransportationnetworksandrespiratoryneuronalnetworks,followpowerlaws.Thesignificanceofpowerlawswithrespecttoothernetworkperformancemeasures,suchasthroughputandsynchronization,rema
3、insanopenquestion.Evolvingmethodsfortheanalysisanddesignofairtransportationnetworksmustbeabletoaddressnetworkperformanceinthefaceofincreasingdemandsandtheneedtocontainandcontrollocalnetworkdisturbances,suchascongestion.Towardthisend,weinvestigatefunctionalrelationshipsthatgoverntheperfo
4、rmanceoftransportnetworks;forexample,thelinksbetweenthefirstnontrivialeigenvalue,λ2,ofanetwork’sLaplacianmatrix—aquantitativemeasureofnetworksynchronizability—andotherglobalnetworkparameters.Inparticular,amongnetworkswithafixeddegreedis-tributionandfixednetworkassortativity(ameasureofanetw
5、ork’spreferencetoattachnodesbasedonasimilarityordifference),thosewithsmallλ2areshowntobepoorsynchronizers,tohavemuchlongershortestpathsandtohavegreaterclusteringincomparisontothosewithlargeλ2.Asimulationofarespiratorynetworkaddsdatatoourinvestigation.Thisstudyisabeginningstepindevelopin
6、gmetricsanddesignvariablesfortheanalysisandactivedesignofairtransportnetworks.©2008WileyPeriodicals,Inc.Complexity00:000–000,2008KeyWords:networks;powerlaws;degreedistribution;synchronization1.INTRODUCTIONbyBarabási[4]andSixDegreesbyWatts[5].AnumberofheUSandworld-wideairtransportnetwork
7、sarescale-excellentreviewarticles,includingNewman[6],Strogatz[7],free1,i.e.,theirdegreedistributionsfollowpowerlawsAlbertandBarabási[8],andDorogovtsevandMendes[9],T[2,3].Alargebodyofrecentworkhasbeenpublishedcontainhundredsofreferences.onscale-freenetworksincludingthepopularboo
