analysis-of-the-airport-network-of-India-as-a-comp

analysisoftheairportnetworkofIndiaasacomplexweightednetworkGaneshBagler,a,aNationalCentreforBiologicalSciences,TataInstituteofFundamentalResearch,Bangalore560065,IndiaReceived15November2007;revised30December2007.Availableonline18January2008.AbstractTransportationinfrastructureofacountryisoneofthemostimportantindicatorsofitseconomicgrowth.HerewestudytheAirportNetworkofIndia(ANI)whichrepresentsIndia’sdomesticcivilaviationinfrastructureasacomplexnetwork.WefindthatANI,anetworkofdomesticairportsconnectedbyairlinks,isasmall-worldnetworkcharacterizedbyatruncatedpower-lawdegreedistributionandhasasignatureofhierarchy.WeinvestigateANIasaweightednetworktoexploreitsvariouspropertiesandcomparethemwiththeirtopologicalcounterparts.ThetrafficinANI,asintheWorld-wideAirportNetwork(WAN),isfoundtobeaccumulatedoninterconnectedgroupsofairportsandisconcentratedbetweenlargeairports.IncontrasttoWAN,ANIisfoundtobehavingdisassortativemixingwhichisoffsetbythetrafficdynamics.Theanalysisindicatespossiblemechanismofformationofanationaltransportationnetwork,whichisdifferentfromthatonaglobalscale.Keywords:Complexnetwork;Transportation;AirportnetworkPACSclassificationcodes:89.75.-k;89.40.Dd;89.75.FbArticleOutline1.Introduction2.AirportNetworkofIndia(ANI)2.1.UnweightedANI2.2.WeightedANI3.TopologicalanalysisofunweightedANI3.1.Shortestpathsanalysis3.2.Degreedistribution4.CentralityinweightedANI5.StructuralorganizationinweightedANI5.1.Clusteringcoefficient5.2.Degreecorrelations6.ConclusionsAcknowledgementsReferences1.IntroductionTransportationinfrastructuresareofcrucialimportancetothedevelopmentofacountry[13]andareimportantindicatorsofitseconomicgrowth.Theyformthebackboneoftourismindustry,supportmovementofgoodsandpeopleacrossthecountry,therebydrivingthenationaleconomy.Roadways,railways,andairwaysarethemajormeansoftransportinIndia,althoughcontributionofairwaysissmallcomparedtothatoftheothertwo.ThecivilaviationsectorinIndiahasbeendevelopingsteadilyandisexpectedtogrowatanacceleratedpacewiththeshiftinthepolicyofthegovernment,andtheadditionofseverallow-costprivateairserviceproviders[16].Theseprivateplayersoffercompetitivepricingandprovidemoreregion-orientedservices,therebyhelpingtoincreasetheairtraffic.Understandingofthesetransportationsystemsisimportantforreasonsofpolicy,administrationandefficiency.Duringthepastfewyears,complexnetworkanalysishasbeenusedtostudytransportationsystems(railways[17]andairlines[2],[9],[10],[4],[8]and[21]),whichareman-madeinfrastructures–fromdifferentaspects–apartfrommanyothersystemsofdiverseorigins[1]and[7].TheWorldwideAirportNetwork(WAN)hasbeenstudiedfromtopologicalaswellastrafficdynamicsperspective.WANhasbeenstudied[2]foritsdegreedistributionandamodelwithconstraints(suchascostofaddinglinkstothenodesorthelimitedcapacityofnodes)wasproposedtoaccountforthetruncationforhigh-degreesinitsscale-freecumulativedegreedistribution.Ithasbeenobserved[9]thatinWAN,mostconnectednodesarenotnecessarilythemost“central”–nodesthroughwhichmostoftheshortestpathsgo.Amodel,incorporatingthegeo-politicalconstraints,hasbeenproposed[8]toexplainthisapparentlysurprisingresult.Beyondthetopologicalfeatures,WANwasstudied[4]inmoredetailbyconsideringthetrafficdynamics–strengthofinteractionsbetweennodes.Amodelwasproposed[5]fortheevolutionofweightedevolvingnetworksinanefforttounderstandthestatisticalpropertiesofreal-worldsystems.AirportNetworkofChina(ANC)[10]–anetworkmuchsmallerthanWAN–wasalsoanalyzedforitstopologyandtrafficdynamics.Itstopologywasfoundtobehavingsmall-worldnetworkfeaturesandatwo-regimepower-lawdegreedistribution.WeinvestigateIndia’sdomesticairportnetworkwhichcomprisesairservicesofallmajorcivilairserviceproviders.Westudythenetworkforitstopologicalfeaturesandforitstrafficdynamics,byconsideringtheintensityofinteractions.First,westudythenetworkasan“unweightednetwork”toinvestigateitstopologicalproperties.Thisnetworkisformedbyconsideringwhetherornotapairofairportsareconnectedbyanairline.Asinmanyothercomplexnetworks,thedetailsofflowofinformationisacrucialfactorforairportnetworks.Hencewestudy“weightednetwork”,inwhichweconsiderthenumberofflightsplyingbetweenanytwoairportsperweek.“Unweightednetwork”representsthearchitecture(topology)ofairports’connectivity,whereas“weightednetwork”representstrafficdynamicsinthenetwork.OuranalysisshowsthatwhileANIissimilartotheWANinsomeaspects,ithasdifferencesinsomefeaturesasreflectedinitsnetworkparameters.WefindthatANIhassmall-world[19]networkfeaturesandhasascale-free[3]degreedistribution.ThetrafficinANIisfoundtobeaccumulatedoninterconnectedgroupsofairportsandisconcentratedontrunkroutesbetweenlargeairports.Itisfoundtobehavingadisassortativetopology,incontrasttoWAN.2.AirportNetworkofIndia(ANI)TheAirportNetworkofIndia(ANI)comprisesdomesticairportsofIndiaandairlinesconnectingthem.TheairservicesprovidedinANIincludeallmajordomesticairserviceprovidersinIndia,includingsomeinternationalairlineswhichplydomesticroutes.Thedatawasobtainedfromatimetable(EXCEL’sTimetableforairserviceswithinIndia,1ason12thJanuary2004)ofairservices,whi