Statistical analysis of airport network of China.

Through the study of airport network of China (ANC), composed of 128 airports (nodes) and 1165 flights (edges), we show the topological structure of ANC conveys two characteristics of small worlds, a short average path length (2.067) and a high degree of clustering (0.733). The cumulative degree distributions of both directed and undirected ANC obey two-regime power laws with different exponents, i.e., the so-called double Pareto law. In-degrees and out-degrees of each airport have positive correlations, whereas the undirected degrees of adjacent airports have significant linear anticorrelations. It is demonstrated both weekly and daily cumulative distributions of flight weights (frequencies) of ANC have power-law tails. Besides, the weight of any given flight is proportional to the degrees of both airports at the two ends of that flight. It is also shown the diameter of each subcluster (consisting of an airport and all those airports to which it is linked) is inversely proportional to its density of connectivity. Efficiency of ANC and of its subclusters is measured through a simple definition. In terms of that, the efficiency of ANC's subclusters increases as the density of connectivity does. ANC is found to have an efficiency of 0.484.

[1]  Charles Gide,et al.  Cours d'économie politique , 1911 .

[2]  Béla Bollobás,et al.  Random Graphs , 1985 .

[3]  K. Christensen,et al.  Evolution of Random Networks , 1998 .

[4]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[5]  Albert-László Barabási,et al.  Internet: Diameter of the World-Wide Web , 1999, Nature.

[6]  Different hierarchy of avalanches observed in the bak-sneppen evolution model , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[7]  T. Ito,et al.  Toward a protein-protein interaction map of the budding yeast: A comprehensive system to examine two-hybrid interactions in all possible combinations between the yeast proteins. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[9]  R. Albert,et al.  The large-scale organization of metabolic networks , 2000, Nature.

[10]  Exact equations and scaling relations for f0 avalanche in the Bak-Sneppen evolution model. , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[11]  L. Amaral,et al.  The web of human sexual contacts , 2001, Nature.

[12]  M. Newman,et al.  Random graphs with arbitrary degree distributions and their applications. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  R Pastor-Satorras,et al.  Dynamical and correlation properties of the internet. , 2001, Physical review letters.

[14]  A. Barabasi,et al.  Weighted evolving networks. , 2001, Physical review letters.

[15]  Ricard V. Solé,et al.  Complexity and fragility in ecological networks , 2000, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[16]  Ramon Ferrer i Cancho,et al.  The small world of human language , 2001, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[17]  M E Newman,et al.  Scientific collaboration networks. I. Network construction and fundamental results. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[19]  M. Newman,et al.  Scientific collaboration networks. II. Shortest paths, weighted networks, and centrality. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  R. F. Cancho,et al.  Topology of technology graphs: small world patterns in electronic circuits. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  S. N. Dorogovtsev,et al.  Evolution of networks , 2001, cond-mat/0106144.

[22]  M E J Newman.  Assortative mixing in networks. , 2002, Physical review letters.

[23]  M. Newman,et al.  Mixing patterns in networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  W. Reed.  The Pareto law of incomes—an explanation and an extension , 2003 .