Abstract
A model of highway networks is proposed which is based on the generalization of the concept of geographical networks to incorporate several of the intermediate towns found between two main localities. This model is validated with respect to the US highway network by comparing a large number of topological measurements extracted from that structure with respective measurements obtained from ensembles of networks produced by the proposed model as well as by more traditional theoretical models of complex networks. An optimal multivariate statistical method, namely canonical analysis, is applied in order to reduce the high dimensionality of the measurements space to allow visualization as well as redundancy reduction and enhanced stochastic sampling. Maximum likelihood decision theory is then applied over the reduced measurement space in order to identify the best models. The results corroborate that the currently proposed model allows the best adherence, among all the other considered models, to the original US highway network.
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References
da Fontoura Costa, L., Oliveira Jr, O.N., Travieso, G., Rodrigues, F.A., Villas Boas, P.R., Antiqueira, L., Viana, M.P., da Rocha, L.E.C.: Analyzing and Modeling Real-World Phenomena with Complex Networks: A Survey of Applications (2008) arXiv:0711.3199
Erdős, P., Rényi, A.: On random graphs. Publicationes Mathematicae 6, 290–297 (1959)
Barabási, A.-L., Albert, R.: Emergence of scaling in random networks. Science 286(5439), 509–512 (1999)
Barabási, A.-L.: The Architecture of Complexity. Control Systems Magazine, IEEE 27(4), 33–42 (2007)
Vázquez, A., Flammini, A., Maritan, A., Vespignani, A.: Modeling of protein interaction networks. Complexus 1(1), 38–44 (2003)
Yook, S.-H., Jeong, H., Barabási, A.-L.: Modeling the Internet’s large-scale topology. Proceedings of the National Academy of Sciences 99(21), 13382–13386 (2002)
Markošová, M.: Network model of human language. Physica A 387(2-3), 661–666 (2008)
da Fontoura Costa, L., Rodrigues, F.A., Travieso, G., Villas Boas, P.R.: Characterization of complex networks: A survey of measurements. Advances in Physics 56(1), 167 (2007)
Albert, R., Albert, I., Nakarado, G.L.: Structural vulnerability of the North American power grid. Physical Review E 69(2), 025103 (2004)
da Fontoura Costa, L., Sporns, O.: Correlating thalamocortical connectivity and activity. Applied Physics Letters 89, 13903 (2006)
Seaton, K.A., Hackett, L.M.: Stations, trains and small-world networks. Physica A 339(3-4), 635–644 (2004)
Gastner, M.T., Newman, M.E.J.: The spatial structure of networks. The European Physical Journal B-Condensed Matter 49(2), 247–252 (2006)
Latora, V., Marchiori, M.: Is the Boston subway a small-world network? Physica A 314(1-4), 109–113 (2002)
Ravasz, E., Barabási, A.-L.: Hierarchical organization in complex networks. Physical Review E 67(2), 26112 (2003)
da Fontoura Costa, L.: The Path-Star Transformation and its Effects on Complex Networks (2007) arXiv:0711.1271
Boccaletti, S., Latora, V., Moreno, Y., Chavez, M., Hwang, D.U.: Complex networks: Structure and dynamics. Physics Reports 424(4-5), 175–308 (2006)
Pastor-Satorras, R., Vázquez, A., Vespignani, A.: Dynamical and correlation properties of the internet. Physical Review Letters 87(25), 258701 (2001)
Newman, M.E.J.: Assortative mixing in networks. Physical Review Letters 89(20), 208701 (2002)
Freeman, L.C.: Centrality in social networks: Conceptual clarification. Social Networks 1, 215–239 (1979)
Girvan, M., Newman, M.E.J.: Community structure in social and biological networks. Proceedings of the National Academy of Sciences of the United States of America 99(12), 7821–7826 (2002)
da Fontoura Costa, L.: The hierarchical backbone of complex networks. Physical Review Letters 93(9), 98702 (2004)
da Fontoura Costa, L., da Rocha, L.E.C.: A generalized approach to complex networks. The European Physical Journal B-Condensed Matter 50(1), 237–242 (2006)
Johnson, R.A., Wichern, D.W.: Applied Multivariate Statistical Analysis. Prentice-Hall, Englewood Cliffs (1998)
Campbell, N.A., Atchley, W.R.: The geometry of canonical variate analysis. Syst. Zool 30(3), 268–280 (1981)
da Fontoura Costa, L., Cesar Jr., R.M.: Shape Analysis and Classification: Theory and Practice. CRC Press, Boca Raton (2001)
Duda, R.O., Hart, P.E., Stork, D.G.: Pattern Classification. Wiley-Interscience, Hoboken (2000)
Bishop, C.M.: Pattern Recognition and Machine Learning (Information Science and Statistics). Springer, New York (2006)
McLachlan, G.J.: Discriminant analysis and statistical pattern recognition. Wiley, New York (1992)
Watts, D.J., Strogatz, S.H.: Collective dynamics of small-world networks. Nature 393(6684), 440–442 (1998)
Waxman, B.M.: Routing of multipoint connections. IEEE Journal on Selected Areas in Communications 6(9), 1617–1622 (1988)
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Villas Boas, P.R., Rodrigues, F.A., da Fontoura Costa, L. (2009). Modeling Highway Networks with Path-Geographical Transformations. In: Fortunato, S., Mangioni, G., Menezes, R., Nicosia, V. (eds) Complex Networks. Studies in Computational Intelligence, vol 207. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01206-8_10
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