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The United States air transportation network analysis Dorothy Cheung

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Introduction The problem and its importance Missing Pieces Related works in summary Methodology – Data set – Network Generation – Network Analysis Conclusion

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Outline The problem and its importance Missing Pieces Related works Methodology – Data set – Network Generation – Network Analysis Conclusion

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The problem and its importance Problem – Analysis the air transportation network in the U.S. Network driven by profits and politics Better understand the network structure not maximize utility Importance – Economy: transport of good and services – Air traffic flow: convenience – Health studies: propagation of diseases

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Outline The problem and its importance Missing Pieces Related works Methodology – Data set – Network Generation – Network Analysis Conclusion

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Missing pieces Sufficient amount of researches on the network with focuses on utility optimization. Commercial enterprises: OAG and Innovata But … lack of research on analyzing the network features studied in class.

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Outline The problem and its importance Missing Pieces Related works Methodology – Data set – Network Generation – Network Analysis Conclusion

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Related works Air transportation networks analysis WAN – World-wide Airport Network ANI – Airport Network of India ANC – Airport Network of China

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Related works Summary: Features of air transportation networks Small world network (compared with random graphs) – Small average shortest path – High average clustering coefficient – Degree mixing differs Scale free power law degree distribution WANANIANC Avg. shortest path4.442.067 Avg. Clustering Coef.0.620.65740.733 Degree mixingAssociativeDissociative WANANIANC Power law exponent 1.02.2 +/- 0.11.65

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Outline The problem and its importance Missing Pieces Related works Methodology – Data set – Network Generation – Network Analysis Conclusion

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Methodology Data Set Network Generation Network Analysis

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Methodology – Data Set Legends OAI : Office of Airline Information RITA : Research and Innovative Technology Administration BTS : Bureau of Transportation Statistics T100 OAI RITA BTS DATABASE My data

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Methodology – Data Set Domestic Air Traffic Hubs [1]

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Methodology – Data Set Domestic scheduled flights – Passengers, cargos, and mails – Military excluded Market Data vs. Segment Data – Market : Used Accounts for passenger once on the same flight number – Segment : Not used Accounts for passenger more than once per leg Month specific : July 2011

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Methodology – Data Set Relevant information Number of Passengers Number of Cargos : Freight and Mail Origin City Destination City PASSENGE RSFREIGHTMAILORIGIN_CITY_NAMEDEST_CITY_NAME DEST_CITY _NUM DEST_STAT E_ABR DEST_STAT E_FIPS DEST_STAT E_NMDEST_WACYEARQUARTERMONTH DISTANCE_ GROUPCLASS 5970017Akhiok, AKKodiak, AK1017AK2Alaska12011371F 192002Akhiok, AKKodiak, AK1017AK2Alaska12011371L 2400Akhiok, AKKodiak, AK1017AK2Alaska12011371F 200Akiachak, AKAkiak, AK1024AK2Alaska12011371F 176477482250Adak Island, AKAnchorage, AK1029AK2Alaska12011373F 2000Adak Island, AKAnchorage, AK1029AK2Alaska12011373L 10528320Akiachak, AKBethel, AK1055AK2Alaska12011371F Sample.csv from BTS

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Methodology – Network Generation Network – 850 Nodes: airports – 21405 entries Weighted edges: sum of passengers and cargos – Directed and Undirected network input files for Pajak [2] and GUESS [5].

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Methodology – Network Generation Microsoft.Jet.OLEDB 4.0Provider ParseCSV GenerateNwk Data Table.CSV PajekDirected.net PajekUndirected.net GUESSDirected.gdf GUESSUndirected.gdf LINQ Network Generation Tool written in C# using LINQ (Language Integrated Query)

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Methodology – Network Generation The U.S. Air Transportation Network drawn in Pajek

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Methodology – Network Analysis Metrics – Degree distributions and correlations Top 10 most connected cities Top 10 most central cites – Small world network? Shortest path length Clustering coefficient Compare against WAN, ANI, and ANC – Cumulative degree distribution and the power law – Resilience – Associativity : Rich-club? – Random graph – Z-Score TBD?

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Methodology – Network Analysis – Degree distributions and correlations Directed network Pajek: In degree : Net -> Partitions -> Degree -> Input Out degree : Net -> Partitions -> Degree -> Output Both : Net -> Partitions -> Degree -> All – Shortest path length Directed network Pajek: Net -> Paths between 2 vertices -> Diameter – Clustering coefficient Directed network Pajek: Net -> Paths between 2 vertices -> Diameter

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Methodology – Network Analysis – Cumulative degree distribution and the power law Directed network Step 1 in Pajek: – Create a partition of all degree – Export the partition in a tab delimited file Tools -> Export to Tab Delimited File -> Current Partition Step 2 in MatLab [6]: – Generating a power law integer distribution X = GetInput.m : reads the partition from the tab delimited file (X => X.name, X.label, X.degree) – Calculating the cumulative distribution cumulativecounts.m [4] [xlincumulative,ylincumulative] = cumulativecounts(X.degree)

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Methodology – Network Analysis – Resilience What % of nodes are removed to reduce the size of the Giant component by half? Consider: – Random attack – Targeted attack : remove nodes with the highest degree and betweenness centrality measures Undirected network with 850 nodes GUESS toolbars: resiliencedegree.py and resiliencebetweenness.py that are downloaded from cTools [4] Compare against a random network (Random and targeted attacks) GUESS : makeSimpleRandom(numberOfNodes, numberOfEdges) => numberOfNodes = 850 numberOfEdges = 21405

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Methodology – Network Analysis – Associativity : Rich-club? Draw conclusion from graphical analysis in GUESS – Random graph Difficulty in constructing a realistic random network that models the real network [3]. – Z-Score? To Be Determined.

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Methodology – Network Analysis Expectations/Predictions – Larger degree nodes are more central (betweenness). Consider LAX, SFO, HOU, JFK, etc. – Small world as compared to WAN, ANI, and ANC – Scale free power law distribution – Dissociate

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Outline The problem and its importance Missing Pieces Related works Methodology – Data set – Network Generation – Network Analysis Conclusion

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The United States air transportation network analysis The problem and its importance Missing Pieces Related works – WAN, ANI, ANC Methodology Data set : BTS : Bureau of Transportation Statistics Network Generation : Directed and Undirected network input files Network Analysis : Degree distribution Small world network as compared to WAN, ANI, and ANC Cumulative degree distribution and power law Resilience Associativity z-score – TBD?

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References for this presentation 1.T-100 reporting guide, RITA, http://www.rita.dot.gov/, www.transtats.bts.gov, http://www.bts.gov/programs/airline_information/.http://www.rita.dot.gov/www.transtats.bts.gov http://www.bts.gov/programs/airline_information/ 2.Pajak, program for large network analysis, http://vlado.fmf.uni- lj.si/pub/networks/pajek/.http://vlado.fmf.uni- lj.si/pub/networks/pajek/ 3.Albert-Laszlo Barabasi and Reka Albert, “Emergence of Scaling in Random Networks”, Department of Physics, University of Notre-Dame, October, 1999. 4.CTools, https://ctools.umich.edu/portal.https://ctools.umich.edu/portal 5.GUESS, graph exploration system, http://graphexploration.cond.org/.http://graphexploration.cond.org/ 6.Matlab, The language of technical computing, http://www.mathworks.com/products/matlab/index.html http://www.mathworks.com/products/matlab/index.html

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