Structural properties of urban bus and subway networks of Madrid

Previous Article
Effects of topology on robustness in ecological bipartite networks
NHM Home
This Issue
Next Article
Bipartite networks provide new insights on international trade markets

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

Structural properties of urban bus and subway networks of Madrid

Mary Luz Mouronte ^1, and Rosa María Benito ^2,

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

Abstract
Related Papers

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.

Keywords: Graph, robustness, betweenness, network science, communities..

Mathematics Subject Classification: Primary: 05C82, 68R10; Secondary: 93A1.

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.

[1]	Liu Hui, Lin Zhi, Waqas Ahmad. Network(graph) data research in the coordinate system. Mathematical Foundations of Computing, 2018, 1 (1) : 1-10. doi: 10.3934/mfc.2018001
[2]	Deena Schmidt, Janet Best, Mark S. Blumberg. Random graph and stochastic process contributions to network dynamics. Conference Publications, 2011, 2011 (Special) : 1279-1288. doi: 10.3934/proc.2011.2011.1279
[3]	Georgy P. Karev. Dynamics of heterogeneous populations and communities and evolution of distributions. Conference Publications, 2005, 2005 (Special) : 487-496. doi: 10.3934/proc.2005.2005.487
[4]	Robert Stephen Cantrell, King-Yeung Lam. Competitive exclusion in phytoplankton communities in a eutrophic water column. Discrete and Continuous Dynamical Systems - B, 2021, 26 (4) : 1783-1795. doi: 10.3934/dcdsb.2020361
[5]	Jelena Grbić, Jie Wu, Kelin Xia, Guo-Wei Wei. Aspects of topological approaches for data science. Foundations of Data Science, 2022, 4 (2) : 165-216. doi: 10.3934/fods.2022002
[6]	A. Marigo. Robustness of square networks. Networks and Heterogeneous Media, 2009, 4 (3) : 537-575. doi: 10.3934/nhm.2009.4.537
[7]	Daniel Ryan, Robert Stephen Cantrell. Avoidance behavior in intraguild predation communities: A cross-diffusion model. Discrete and Continuous Dynamical Systems, 2015, 35 (4) : 1641-1663. doi: 10.3934/dcds.2015.35.1641
[8]	Emiliano Alvarez, Juan Gabriel Brida, Lucía Rosich, Erick Limas. Analysis of communities of countries with similar dynamics of the COVID-19 pandemic evolution. Journal of Dynamics and Games, 2022, 9 (1) : 75-96. doi: 10.3934/jdg.2021026
[9]	Luis Barreira, Claudia Valls. Noninvertible cocycles: Robustness of exponential dichotomies. Discrete and Continuous Dynamical Systems, 2012, 32 (12) : 4111-4131. doi: 10.3934/dcds.2012.32.4111
[10]	Eric Babson and Dmitry N. Kozlov. Topological obstructions to graph colorings. Electronic Research Announcements, 2003, 9: 61-68.
[11]	Oded Schramm. Hyperfinite graph limits. Electronic Research Announcements, 2008, 15: 17-23. doi: 10.3934/era.2008.15.17
[12]	J. William Hoffman. Remarks on the zeta function of a graph. Conference Publications, 2003, 2003 (Special) : 413-422. doi: 10.3934/proc.2003.2003.413
[13]	John Kieffer and En-hui Yang. Ergodic behavior of graph entropy. Electronic Research Announcements, 1997, 3: 11-16.
[14]	Roberto De Leo, James A. Yorke. The graph of the logistic map is a tower. Discrete and Continuous Dynamical Systems, 2021, 41 (11) : 5243-5269. doi: 10.3934/dcds.2021075
[15]	Desheng Li, P.E. Kloeden. Robustness of asymptotic stability to small time delays. Discrete and Continuous Dynamical Systems, 2005, 13 (4) : 1007-1034. doi: 10.3934/dcds.2005.13.1007
[16]	Cristopher Hermosilla. Stratified discontinuous differential equations and sufficient conditions for robustness. Discrete and Continuous Dynamical Systems, 2015, 35 (9) : 4415-4437. doi: 10.3934/dcds.2015.35.4415
[17]	Juan Manuel Pastor, Silvia Santamaría, Marcos Méndez, Javier Galeano. Effects of topology on robustness in ecological bipartite networks. Networks and Heterogeneous Media, 2012, 7 (3) : 429-440. doi: 10.3934/nhm.2012.7.429
[18]	Florian Dumpert. Quantitative robustness of localized support vector machines. Communications on Pure and Applied Analysis, 2020, 19 (8) : 3947-3956. doi: 10.3934/cpaa.2020174
[19]	Mingxing Zhou, Jing Liu, Shuai Wang, Shan He. A comparative study of robustness measures for cancer signaling networks. Big Data & Information Analytics, 2017, 2 (1) : 87-96. doi: 10.3934/bdia.2017011
[20]	Rubén Caballero, Alexandre N. Carvalho, Pedro Marín-Rubio, José Valero. Robustness of dynamically gradient multivalued dynamical systems. Discrete and Continuous Dynamical Systems - B, 2019, 24 (3) : 1049-1077. doi: 10.3934/dcdsb.2019006

2020 Impact Factor: 1.213

Tools

Metrics

Other articles
by authors

on AIMS
Mary Luz Mouronte Rosa María Benito
on Google Scholar
Mary Luz Mouronte Rosa María Benito

[Back to Top]