Abstract
Many transport processes on network depend crucially on the underlying network topology. In this paper, we propose a model to generate correlated scale free transportation networks with community structure by considering the mechanisms of dynamical network evolution and rewiring links. With the introduction of congestion effects, we investigate the performance and carrying capacity of this network. The results show that congestion in the uncorrelated network is more serious than the assortative or disassortative ones. Therefore, the correlated network with communities can bear much more traffic flow. In addition, the networks with lager modularity can enhance the transportation efficiently.
Similar content being viewed by others
References
Pastor-Satorras, R., Vázquez, A., Vespignani, A.: Dynamical and correlation properties of the Internet. Phys. Rev. Lett. 87, 258701 (2001)
Wang, J.Y., Feng, J.W., Xu, C., Zhao, Y.: Cluster synchronization of nonlinearly-coupled complex networks with nonidentical nodes and asymmetrical coupling matrix. Nonlinear Dyn. 67(2), 1635–1646 (2012)
Newman, M.E.J.: The structure and function of complex networks. SIAM Rev. 45, 167–256 (2003)
Lü, L., Li, C.R.: Generalized synchronization of spatiotemporal chaos in a weighted complex network. Nonlinear Dyn. 63(4), 699–710 (2011)
Liang, J.L., Wang, Z.D., Liu, X.H.: Exponential synchronization of stochastic delayed discrete-time complex networks. Nonlinear Dyn. 53(1–2), 153–165 (2008)
Wu, J.J., Sun, H.J., Gao, Z.Y.: Dynamic urban traffic flow behavior on scale-free networks. Physica A 387, 653–660 (2008)
Ito, T., Chiba, T., Ozawa, R., Yoshida, M., Hattori, M., Sakaki, Y.: A comprehensive two-hybrid analysis to explore the yeast protein interactome. Proc. Natl. Acad. Sci. USA 98, 4569–4574 (2001)
Girvan, M., Newman, M.E.J.: Community structure in social and biological networks. Proc. Natl. Acad. Sci. USA 99, 7821–7826 (2002)
Guimerà, R., Mossa, S., Turtschi, A., Amaral, L.A.: The worldwide air transportation network: anomalous centrality, community structure, and cities’ global roles. Proc. Natl. Acad. Sci. USA 102(22), 7794–7799 (2005)
Fortunato, S., Latora, V., Marchiori, M.: A method to find community structure based on information centrality. Phys. Rev. E 70, 056104 (2004)
Arenas, A., Díaz-Guilera, A., Pérez-Vicente, C.: Synchronization reveals topological scales in complex networks. Phys. Rev. Lett. 96, 114102 (2006)
Wu, J.J., Gao, Z.Y., Sun, H.J.: Cascade and breakdown in scale-free networks with community structure. Phys. Rev. E 74, 066111 (2006)
Kitchovitch, S., Liò, P.: Community structure in social networks: applications for epidemiological modelling. PLoS ONE 6(7), 22220 (2011)
Newman, M.E.J.: Assortative mixing in networks. Phys. Rev. Lett. 89, 208701 (2002)
Capocci, A., Caldarelli, G., Rios, P.D.L.: Quantitative description and modeling of real networks. Phys. Rev. E 68, 047101 (2003)
Sorrentino, F., di Bernardo, M., Huerta-Cuellar, G., Boccaletti, S.: Synchronization in weighed scale free networks with degree-degree correlation. Physica D 224, 123–129 (2006)
Xue, Y.H., Wang, J., Li, L., He, D.R., Hu, B.B.: Optimizing transport efficiency on scale-free networks through assortative or dissortative topology. Phys. Rev. E 81, 037101 (2010)
Sun, J.T., Wang, S.J., Huang, Z.G., Wang, Y.H.: Effect of degree correlations on networked traffic dynamics. Physica A 388, 3244–3248 (2009)
Menche, J., Valleriani, A., Lipowsky, R.: Dynamical processes on dissortative scale-free networks. Europhys. Lett. 89, 18002 (2010)
Newman, M.E.J., Girvan, M.: Finding and evaluating community structure in networks. Phys. Rev. E 69, 026113 (2004)
Lancichinetti, A., Fortunato, S.: Community detection algorithms: a comparative analysis. Phys. Rev. E 80, 056117 (2009)
Barabási, A.L., Albert, R.: Emergence of scaling in random networks. Science 286, 509–512 (1999)
Maslov, S., Sneppen, K.: Specificity and stability in topology of protein networks. Science 296, 910–913 (2002)
Sheffi, Y.: Urban Transportation Networks: Equilibrium Analysis with Mathematical Programming Methods. Prentice-Hall, Englewood Cliffs (1985)
Wu, J.J., Gao, Z.Y., Sun, H.J., Huang, H.J.: Congestion in different topologies of traffic networks. Europhys. Lett. 74, 560 (2006)
Wu, J.J., Sun, H.J., Gao, Z.Y.: Cascading failures on weighted urban traffic equilibrium networks. Physica A 386, 407–413 (2007)
Latora, V., Marchiori, M.: Efficient behavior of small-world networks. Phys. Rev. Lett. 87, 198701 (2001)
Acknowledgements
This paper is partly supported by National Basic Research Program of China (2012CB725401), NSFC (71131001), NSF of Beijing (8102029), the Fundamental Research Funds for the Central Universities (2012JBZ005), and the Program for New Century Excellent Talents in University (NCET-09-0208), and FANEDD (201170).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Sun, Hj., Zhang, H. & Wu, Jj. Correlated scale-free network with community: modeling and transportation dynamics. Nonlinear Dyn 69, 2097–2104 (2012). https://doi.org/10.1007/s11071-012-0411-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11071-012-0411-5