Abstract
The U.S. airline network is one of the most advanced transportation infrastructures in the world. It is a complex geospatial structure that sustains a variety of dynamics including commercial, public, and military operations and services. We study the U.S. domestic intercity passenger air transportation network using a weighted complex network methodology, in which vertices represent cities and edges represent intercity airline connections weighted by average daily passenger traffic, non-stop distance, and average one-way fares. We find that U.S. intercity passenger air transportation network is a small-world network accompanied by dissortative mixing patterns and rich-club phenomenon, implying that large degree cities (or hub cities) tend to form high traffic volume interconnections among each other and large degree cities tend to link to a large number of small degree cities. The interhub air connections tend to form interconnected triplets with high traffic volumes, long non-stop distances, and low average one-way fares. The structure of the U.S. airline network reflects the dynamic integration of pre-existing urban and national transportation infrastructure with the competitive business strategies of commercial airlines. In this paper we apply an emerging methodology to representing, analyzing, and modeling the complex interactions associated with the physical and human elements of the important U.S. national air transport and services infrastructure.













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Alderighi, M., Gento, A., Nijkamp, P., & Rietveld, P. (2005). Network competition—the coexistence of hub-and-spoke and point-to-point systems. Journal of Air Transport Management, 11, 328–334. doi:10.1016/j.jairtraman.2005.07.006.
Bagler, G. (2008). Analysis of the airport network of India as a complex weighted network. Physica A, 387(12), 2972–2980.
Bania, N., Bauer, P. W., & Zlatoper, T. J. (1998). U.S. air passenger service: A taxonomy of route networks, hub locations, and competition. Transportation Research E., 34(1), 53–74. doi:10.1016/S1366-5545(97)00037-9.
Barabasi, A. L. (2002). Linked: The new science of networks. Cambridge, MA: Perseus Books Group.
Barabasi, A. L., & Ravasz, E., et al. (2003). Hierarchical organization of modularity in complex networks. In R. Pastor-Satorras, M. Rubi, & A. Diaz-Guilera (Eds.), Statistical mechanics of complex networks (pp. 46–64). Berlin: Springer.
Barrat, A., Barthelemy, M., Pastor-Satorras, R., & Vespignani, A. (2004a). The architecture of complex weighted networks. Proceedings of the National Academy of Sciences of the United States of America, 101(11), 3747–3752. doi:10.1073/pnas.0400087101.
Barrat, A., Barthelemy, M., & Vespignani, A. (2005). The effects of spatial constraints on the evolution of weighted complex networks. Journal of Statistical Mechanics: Theory and Experiment, (05), 05003. doi:10.1088/1742-5468/2005/05/P05003.
Barrat, A., Barthélemy, M., & Vespignani, A. (2004b). Modeling the evolution of weighted networks. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, 70(6), 066149. doi:10.1103/PhysRevE.70.066149.
Barrat, A., Barthélemy, M., & Vespignani, A. (2004c). Weighted evolving networks: Coupling topology and weight dynamics. Physical Review Letters, 92(22), 228701. doi:10.1103/PhysRevLett.92.228701.
Bathelemy, M., Barrat, A., Pastor-Satorras, R., & Vespignani, A. (2005). Characterization and modeling of weighted networks. Physica A, 346, 34–43. doi:10.1016/j.physa.2004.08.047.
Batty, M. (2003). Network geography: Relations, interactions, scaling and spatial processes in GIS. http://www.casa.ucl.ac.uk/working_papers/paper63.pdf. Accessed 20 April 2008.
Brandes, U. (2001). A faster algorithm for betweenness centrality. The Journal of Mathematical Sociology, 25(2), 163–177.
Brandes, U. (2008). On variants of shortest-path betweenness centrality and their generic computation. Social Networks, 30(2), 136–145.
Brueckner, J. K. (2004). Network structure and airline scheduling. The Journal of Industrial Economics, LII(2), 291–312. doi:10.1111/j.0022-1821.2004.00227.x.
Bryan, D., & O’Kelly, M. E. (1999). Hub-and-spoke networks in air transportation: An analytical review. Journal of Regional Science, 39(2), 275–295. doi:10.1111/1467-9787.00134.
Callaway, D. S., Newman, M. E. J., Strogatz, S. H., & Watts, D. J. (2000). Network robustness and fragility: Percolation on random graphs. Physical Review Letters, 85(25), 5468. doi:10.1103/PhysRevLett.85.5468.
Claust, A., Shalizi, C. R., & Newman, M. E. J. (2007). Power-law distributions in empirical data. http://arxiv.org/abs/0706.1062v1. Accessed 14 December 2007.
Costa, L. d. F., Rodrigues, F. A., Travieso, G., & Boas, P. R. V. (2007). Characterization of complex networks: A survey of measurements. Advances in Physics, 56(1), 167–242. doi:10.1080/00018730601170527.
Freeman, L. C. (1977). A set of measures of centrality based on betweenness. Sociometry, 40(1), 35–41. doi:10.2307/3033543.
Gillen, D., & Morrison, W. G. (2005). Regulation, competition and network evolution in aviation. Journal of Air Transport Management, 11, 161–174. doi:10.1016/j.jairtraman.2005.03.002.
Goetz, A. R., & Sutton, C. J. (1997). The geography of deregulation in the U.S. airline industry. Annals of the Association of American Geographers. Association of American Geographers, 87(2), 238–263. doi:10.1111/0004-5608.872052.
Grais, R. F., Ellis, J. H., Kress, A., & Glass, G. E. (2004). Modeling the spread of annual influenza epidemics in the U.S.: The potential role of air travel. Health Care Management Science, 7(2), 127–134. doi:10.1023/B:HCMS.0000020652.38181.da.
Guida, M., & Maria, F. (2007). Topology of the Italian airport network: A scale-free small-world network with a fractal structure? Chaos, Solitons and Fractals, 31, 527–536. doi:10.1016/j.chaos.2006.02.007.
Guimera, R., & Amaral, L. A. N. (2004). Modeling the world-wide airport network. The European Physical Journal B, 38, 381–385. doi:10.1140/epjb/e2004-00131-0.
Guimera, R., Mossa, S., Turtschi, A., & Amaral, L. A. N. (2005). The worldwide air transportation network: Anomalous centrality, community structure, and cities’ global roles. Proceedings of the National Academy of Sciences of the United States of America, 102(22), 7794–7799. doi:10.1073/pnas.0407994102.
Haggett, P., & Chorley, R. J. (1969). Network analysis in geography. New York, NY: St Martin’s Press.
Horner, M., & O’Kelly, M. E. (2001). Embedding economies of scale concepts for hub network design. Journal of Transport Geography, 9(4), 255–265. doi:10.1016/S0966-6923(01)00019-9.
Irwin, M. D., & Kasarda, J. D. (1991). Air passenger linkages and employment growth in U.S. metropolitan areas. American Sociological Review, 56(4), 524–537. doi:10.2307/2096272.
Jaillet, P., Song, G., & Yu, G. (1996). Airline network design and hub location problems. Location Science, 4(3), 195–212. doi:10.1016/S0966-8349(96)00016-2.
Kansky, K. J. (1963). Structure of transportation networks. Chicago, IL: University of Chicago Press.
Lederer, P. J., & Nambimadom, R. S. (1998). Airline network design. Operations Research, 46(6), 785–804.
Li, W., & Cai, X. (2004). Statistical analysis of airport network of China. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, 69(4), 046106. doi:10.1103/PhysRevE.69.046106.
Magnanti, T. L., & Wong, R. T. (1984). Network desgin and transportation planning—models and algorithms. Transportation Science, 18(1), 1–55.
Minouz, M. (1989). Network synthesis and optimum network design problems—models, solutions and applications. Networks, 19(3), 313–360. doi:10.1002/net.3230190305.
Newman, M. E. J. (2001). Scientific collaboration networks. II. Shortest paths, weighted networks, and centrality. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, 64(1), 016132. doi:10.1103/PhysRevE.64.016132.
Newman, M. E. J. (2003). The structure and function of complex networks. SIAM Review, 45, 167–256. doi:10.1137/S003614450342480.
Newman, M. E. J., & Girvan, M. (2004). Finding and evaluating community structure in networks. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, 69(2), 026113. doi:10.1103/PhysRevE.69.026113.
O’Kelly, M. E. (1998). A geographer’s analysis of hub-and-spoke networks. Journal of Transport Geography, 6(3), 171–186. doi:10.1016/S0966-6923(98)00010-6.
O’Kelly, M. E., & Bryan, D. (1998). Hub location with flow economies of scale. Transportation Research Part B: Methodological, 32(8), 605–616. doi:10.1016/S0191-2615(98)00021-6.
O’Kelly, M. E., & Miller, H. (1994). The hub network design problem: A review and synthesis. Journal of Transport Geography, 2(1), 31–40. doi:10.1016/0966-6923(94)90032-9.
Park, K., Lai, Y.-C., & Ye, N. (2004). Characterization of weighted complex networks. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, 70(2), 026109–4. doi:10.1103/PhysRevE.70.026109.
Pred, A. (1977). City systems in advanced societies. New York, NY: Wiley.
Ravasz, E., & Barabási, A.-L. (2003). Hierarchical organization in complex networks. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, 67(2), 026112. doi:10.1103/PhysRevE.67.026112.
Shaw, S.-L. (1993). Hub structures of major US passenger airlines. Journal of Transport Geography, 1(1), 47–58. doi:10.1016/0966-6923(93)90037-Z.
Strogatz, S. H. (2001). Exploring complex networks. Nature, 410(6825), 268–276. doi:10.1038/35065725.
Sui, D. Z. (2006). Geography and the small world: Challenges for GIScience, Geoworld, June, 24–26. Accessed 10 May 2007.
Sui, D. Z. (2007). Geographic information systems and the medical geography: Toward a new synergy. Geography Compass, 1(3), 556–582. doi:10.1111/j.1749-8198.2007.00027.x.
Swan, W. M. (2002). Airline route developments: A review of history. Journal of Air Transport Management, 8, 349–353. doi:10.1016/S0969-6997(02)00015-7.
Vázquez, A., Pastor-Satorras, R., & Vespignani, A. (2002). Large-scale topological and dynamical properties of the Internet. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, 65(6), 066130. doi:10.1103/PhysRevE.65.066130.
Vowles, T. M. (2006). Geographic perspectives of air transportation. The Professional Geographer, 58(1), 12–19. doi:10.1111/j.1467-9272.2006.00508.x.
Watts, D. J. (1999). Small worlds: The dynamics of networks between order and randomness. Princeton, NJ: Princeton University Press.
Watts, D. J. (2004). The “new” science of networks. Annual Review of Sociology, 30, 243–270. doi:10.1146/annurev.soc.30.020404.104342.
Watts, D. J., & Strogatz, S. H. (1998). Collective dynamics of ‘small-world’ networks. Nature, 393, 440–442. doi:10.1038/30918.
Zhou, S., & Mondragon, R. J. (2004). The rich-club phenomenon in the Internet topology. Communication Letters, IEEE, 8(3), 180–182.
Acknowledgment
Support by the president fund in Houston Advanced Research Center for this project is gratefully acknowledged. We would like to thank anonymous reviewers who have provided valuable comments that substantially improved our arguments. We are fully responsible for any remaining errors.
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Xu, Z., Harriss, R. Exploring the structure of the U.S. intercity passenger air transportation network: a weighted complex network approach. GeoJournal 73, 87–102 (2008). https://doi.org/10.1007/s10708-008-9173-5
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DOI: https://doi.org/10.1007/s10708-008-9173-5