September  2012, 7(3): 415-428. doi: 10.3934/nhm.2012.7.415

Structural properties of urban bus and subway networks of Madrid

1. 

Departamento de Ingeniería Telemática, Escuela Politécnica Superior, Universidad Carlos III de Madrid, Ave. Universidad, 30, Edif. Torres Quevedo, Leganés, 28911 Madrid, Spain

2. 

Grupo de Sistemas Complejos and Departamento de Fisica y Mecanica, E.T.S.I. Agrónomos, Universidad Politécnica de Madrid, 28040 Madrid

Received  December 2011 Revised  June 2012 Published  October 2012

The goal of this research is to estimate different parameters in the urban bus and the subway networks of Madrid. The obtained results will allow learning more about both types of networks: modularity, most important stops, sensitivity in the district networks (districts with highest and lowest sensitivity), bus line concentration by detected communities, communication capacity for these networks (districts with the greatest and less number of inner and external communications), and relation between network and dweller density by district. This study can help to improve the transport networks: reducing the district sensitivity, adding new stops or routes, etc.
Citation: Mary Luz Mouronte, Rosa María Benito. Structural properties of urban bus and subway networks of Madrid. Networks and Heterogeneous Media, 2012, 7 (3) : 415-428. doi: 10.3934/nhm.2012.7.415
References:
[1]

J. P. Cardenas, et al., The effect of the complex topology on the robustness of spanish SDH network, in "Fifth International Conference on Networking and Services," IEEE Xplore, (2007), 2289-2301.

[2]

R. Criado, et al., Efficiency, vulnerability and cost: An overview with applications to subway networks worldwide, Int. Journal of Bif. And Chaos, 17 (2007), 2289-2301. doi: 10.1142/S0218127407018397.

[3]

R. Criado, et al., Understanding complex networks through the study of their critical nodes: Efficiency, vulnerability and dynamical importance, in "International Conference on Modelling and Computation on Complex Networks and Related Topics Net-Works 2007," (2007), 23-30.

[4]

B. Fields, et al, Analysis and exploitation of musician social networks for recommendation and discovery, IEEE Transactions on Multimedia, 13 (2011), 674-686. doi: 10.1109/TMM.2011.2111365.

[5]

O. Kwona and W. S. Jung, Intercity express bus flow in Korea and its network analysis, Physica A: Statistical Mechanics and its Applications, 391 (2012), 4261-4265. doi: 10.1016/j.physa.2012.03.031.

[6]

T. Majima, M. Katuhara and K. Takadama, Analysis on transport networks of railway, subway and waterbus in Japan, Emergent Intelligence of Networked Agents Studies in Computational Intelligence, 56 (2007), 99-113. doi: 10.1007/978-3-540-71075-2_8.

[7]

M. E. J. Newman, The structure and function of complex networks, SIAM Review, 45 (2003), 167-256. doi: 10.1137/S003614450342480.

[8]

M. E. J. Newman, Modularity and community structure in networks, Proc. Natl. Acad. Sci. USA, 103 (2006), 8577-8582. doi: 10.1073/pnas.0601602103.

[9]

P. Pons and M. Latapy, Computing communities in large networks using random walks, J. Graph Algorithms Appl., 10 (2006), 191-218. doi: 10.7155/jgaa.00124.

[10]

D. Watts and S. Strogatz, Collective dynamics of 'small-world' networks, Nature, 393 (1998), 440-442. doi: 10.1038/30918.

show all references

References:
[1]

J. P. Cardenas, et al., The effect of the complex topology on the robustness of spanish SDH network, in "Fifth International Conference on Networking and Services," IEEE Xplore, (2007), 2289-2301.

[2]

R. Criado, et al., Efficiency, vulnerability and cost: An overview with applications to subway networks worldwide, Int. Journal of Bif. And Chaos, 17 (2007), 2289-2301. doi: 10.1142/S0218127407018397.

[3]

R. Criado, et al., Understanding complex networks through the study of their critical nodes: Efficiency, vulnerability and dynamical importance, in "International Conference on Modelling and Computation on Complex Networks and Related Topics Net-Works 2007," (2007), 23-30.

[4]

B. Fields, et al, Analysis and exploitation of musician social networks for recommendation and discovery, IEEE Transactions on Multimedia, 13 (2011), 674-686. doi: 10.1109/TMM.2011.2111365.

[5]

O. Kwona and W. S. Jung, Intercity express bus flow in Korea and its network analysis, Physica A: Statistical Mechanics and its Applications, 391 (2012), 4261-4265. doi: 10.1016/j.physa.2012.03.031.

[6]

T. Majima, M. Katuhara and K. Takadama, Analysis on transport networks of railway, subway and waterbus in Japan, Emergent Intelligence of Networked Agents Studies in Computational Intelligence, 56 (2007), 99-113. doi: 10.1007/978-3-540-71075-2_8.

[7]

M. E. J. Newman, The structure and function of complex networks, SIAM Review, 45 (2003), 167-256. doi: 10.1137/S003614450342480.

[8]

M. E. J. Newman, Modularity and community structure in networks, Proc. Natl. Acad. Sci. USA, 103 (2006), 8577-8582. doi: 10.1073/pnas.0601602103.

[9]

P. Pons and M. Latapy, Computing communities in large networks using random walks, J. Graph Algorithms Appl., 10 (2006), 191-218. doi: 10.7155/jgaa.00124.

[10]

D. Watts and S. Strogatz, Collective dynamics of 'small-world' networks, Nature, 393 (1998), 440-442. doi: 10.1038/30918.

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