Developing Graph Centrality Concepts in Analyzing and Prioritizing Transportation Network Components

Document Type : Scientific - Research

Authors
Alireza Mahpour 1
amir hosseinpanahi 2
Hooman rahimi 3
Hassan Divandari 3
1 Transportation Planning, Faculty of Civil, Water and Environmental Engineering, Shahid Beheshti University, Tehran
2 PhD student in civil engineering, transportation planning, Islamic Azad University, central Tehran branch, Tehran, Iran
3 Assistant Professor of Transportation Planning, Department of civil engineering ShQ.C,Islamic azad university,Shahr-e-Qods,Iran
10.22119/jte.2026.536860.2744
Abstract
Identifying key components of urban transportation networks to enhance resilience, reduce vulnerability, and optimize traffic flow is a fundamental issue in transportation planning. In this study, an analytical framework based on graph-theoretical centrality concepts and matrix–tensor structures was developed to determine and prioritize the relative importance of network components. To this end, three incidence matrices—route–street, street–intersection, and route–intersection—were defined, and a three-dimensional tensor was constructed to represent the multilayer relationships of the network simultaneously. Degree, betweenness, and eigenvector centrality measures were then computed based on these structures and integrated through normalization and weighted aggregation. The proposed framework was implemented on the benchmark Nguyen–Dupuis network consisting of 13 nodes and 38 links. The results indicated that nodes 6, 11, and 5 exhibit the highest composite centrality values, and selecting the top five nodes covers 92.3% of the network routes. Sensitivity analysis further revealed that the tensor-based criterion can highlight inter-layer nodes that are not identified by classical methods. The findings suggest that the combined use of incidence matrices and tensor structures provides deeper insight into the functional organization of transportation networks and can support more effective strategies for maintenance prioritization, alternative route design, and system resilience enhancement.
Keywords
Importance of transportation network components
incidence matrix
three-dimensional tensor
centrality concepts
Subjects
- Albert, R., & Barabási, A.L. (2002). Statistical mechanics of complex networks. Rev. Mod. Phys., 74, 47-97.
 
- Albert, R., Jeong, H., & Barabási, A. L. (1999). Internet: Diameter of the world-wide web. Nature, 401, 130–131.
 
- Albert, R., Jeong, H., & Barabási, A. L. (2000). Error and attack tolerance of complex networks. Nature, 406(6794), 378-382.
 
- Amini, M.H., Arasteh, H., & Siano, P. (2019). Sustainable smart cities through the lens of complex interdependent infrastructures: Panorama and state-of-the-art. In Sustainable Interdependent Networks II (pp. 45-68). Springer, Cham, Switzerland.
 
- Arul, S. M., Senthil, G., Jayasudha, S., Alkhayyat, A., Azam, K., & Elangovan, R. (2023) "Graph Theory and Algorithms for Network Analysis", E3S Web of Conferences, Vol. 399, pp. 08002.
 
- Bae, J., & Kim, S. (2014). Identifying and ranking influential spreaders in complex networks by neighborhood coreness. Physica A, 395, 549–559.
 
- Berman, O., Larson, R. C., and Fouska, N. (1992)"Optimal location of discretionary service facilities", Transportation Science, Vol. 26, pp. 201-211-16.
 
- Bonacich, P. (1972). Factoring and weighting approaches to status scores and clique identification. Journal of Mathematical Sociology, 2, 113–120.
 
- Brin, S., & Page, L. (1998). The anatomy of a large-scale hypertextual web search engine. Web Conference, 30, 107–117.
 
- Castillo, E., Jimenez, P., Menéndez, J. M., & Conejo, A. J. (2008). The observability problem in traffic models: algebraic and topological methods. IEEE Transactions on Intelligent Transportation Systems, 9(2), 275 – 28.
 
- Chen, D. B., Lü, L. Y., Shang, M. S., Zhang, Y. C., & Zhou, T. (2012). Identifying influential nodes in complex networks. Physica A, 391.
 
- Luo, L., Yang, Y., Chen, Z. and Wei, Y., 2018. Identifying opinion leaders with improved weighted LeaderRank in online learning communities. International Journal of Performability Engineering, 14(2), p.193.777–1787.
 
- Chen, X., Wang, Y., & Li, J. (2008). Identification of critical nodes in urban traffic networks using complex network theory. Transportation Research Part C: Emerging Technologies, 125, 103018.
 
- Estrada, E., & Rodriguez-Velazquez, J. A. (2005). Subgraph centrality in complex networks. Physical Review E, 71, 056103.
 
- Gryzkov, T., Tortosa, L., Vicent, J. F., & Wilson, R. (2019). A centrality measure for urban networks based on the eigenvector centrality concept. Environment and Planning B: Urban Analytics and City Science, 46(4), 668-689.
 
- Hage, P., & Harary, F. (1995). Eccentricity and centrality in networks. Social Networks, 17, 57–63.
 
- Henry, E., Bonnetain, L., Furno, A., El Faouzi, N.-E., & Zimeo, E. (2019) Spatio-temporal Correlations of Betweenness Centrality and Traffic Metrics, IEEE International Conference on Big Data (Big Data), pp. 4725-4733.
 
- Katz, L. (1953). A new status index derived from sociometric analysis. Psychometrika, 18, 39–43.
- Kirkley, A., Barbosa, H., Barthelemy, M., & Ghoshal, G. (2018). From the betweenness centrality in street networks to structural invariants in random planar graphs. Nature Communications, 9(1), 2501.
 
- Kleinberg, J. M. (1999). Authoritative sources in a hyperlinked environment. Journal of the ACM, 46, 604–632.
 
- Li, L., Lin, X., Ran, B., & Du, B. (2025). Tensor decomposition of transportation temporal and spatial big data: A brief review. Fundamental Research, in press.
 
- Li, Y., Huang, Z., & Wu, J. (2023). Tensor-based centrality measures for dynamic traffic networks. IEEE Transactions on Intelligent Transportation Systems, 24(5), 4782-4795.
 
Lü, L., Zhang, Y.C., Yeung, C.H. and Zhou, T., 2011. Leaders in social networks, the delicious case. PloS one, 6(6), p.e21202.
 
- Weng, J., Lim, E. P., Jiang, J., & He, Q. (2010). Twitterrank: Finding topic-sensitive influential twitterers. In Proceedings of the Third ACM International Conference on Web Search and Data Mining (pp. 261–270). ACM Press: New York, NY, USA.
 
- Lü, L. Y., Zhou, T., Zhang, Q. M., & Stanley, H. E. (2016). The h-index of a network node and its relation to degree and coreness. Nature Communications, 7, 10168.
 
- Mamdoohi, A. R., & Mahpur, A. (2011). Development of incremental traffic assignment algorithm based on variable number of step size: case study of Mashhad. Journal of Traffic Engineering, 12(47), 31-37.
 
- Mamdoohi, A. R., Kamyab, S., & Mahpur, A. (2012b). The effect of zone size on traffic assignment results, case study of Mashhad. Journal of Traffic Engineering, 13(48), 12-18.
 
- Mamdoohi, A. R., Mahpur, A., & Masudi, M. (2011). An economic impact analysis of distance-learning as a transportation demand management strategy for educational trips. Sharif Journal of Civil Engineering, 27-2(3), 17-22.
 
- Mamdoohi, A.R. and Mahpur, A., (2010). Analyzing the effect of number of iterations on incremental traffic assignment results accuracy: case study of mashhad. Journal of Traffic Engineering, 11(44), pp.45-52.
 
- Mamdoohi, A.R., Mahpour, A. and Yousefikia, M., (2012a). Minimum Spanning Tree concept development to the case of loaded networks and its application in transportation analysi. Modares Civil Engineering journal, 12(2), pp.61-69.
 
- Mínguez, R., Sánchez-Cambronero, S., Castillo, E., & Jiménez, P. (2010). Optimal traffic plate scanning location for od trip matrix and route estimation in road networks. Transportation Research Part B: Methodological, 44(2), 282 – 298.
 
- Morone, F., & Makse, H. A. (2015). Influence maximization in complex networks through optimal percolation. Nature, 524, 65–68.
 
- Nie, T. Y., Guo, Z., Zhao, K., & Lu, Z. M. (2016). Using mapping entropy to identify node centrality in complex networks. Physica A, 453, 290–297.
 
- Nikitina, N. N., & Ivashko, E. E. (2024). Calculation of centrality in the analysis of congestion of city roads on the example of Petrozavodsk. Mathematical Game Theory and Applications, 15(3), 41–63.
 
- Peranginangin, A. P. (2024) "Analysis of Graph Theory in Transport Network Optimisation: A Mathematical Approach and Its Applications", Jurnal Educatio, Vol. 10, No. 4, pp. 1431-1439.
 
- Piraveenan, M., & Saripada, N. B. (2023) Transportation Centrality: Quantifying the Relative Importance of Nodes in Transportation Networks Based on Traffic Modeling, IEEE Access, Vol. 11, pp. 142214-142234.
 
- Ruan, Y. R., Lao, S. Y., Wang, J. D., Bai, L., & Chen, L. D. (2017). Node importance measurement based on neighborhood similarity in complex network. Acta Physica Sinica, 66, 38902.
 
- Ruan, Y. R., Lao, S. Y., Xiao, Y. D., Wang, J. D., & Bai, L. (2016). Identifying influence of nodes in complex networks with coreness centrality: Decreasing the impact of densely local connection. Chinese Physics Letters, 33, 028901.
 
- Sabidussi, G. (1966). The centrality index of a graph. Psychometrika, 31, 581–603.
 
- Stephenson, K., & Zelen, M. (1989). Rethinking centrality: Methods and examples. Social Networks, 11, 1–37.
 
- Taylor, D., Myers, S. A., Clauset, A., Porter, M. A., & Mucha, P. J. (2017). Eigenvector-based centrality measures for temporal networks. Multiscale Modeling & Simulation, 15(1), 537-574.
 
- Tepsan, W., Phaphuangwittayakul, A., Sokantika, S., & Harnpornchai, N. (2025) Identifying Hubs Through Influential Nodes in Transportation Network by Using a Gravity Centrality Approach, Algorithms, Vol. 18, pp. 356.
- Wang, L., Zhang, H., & Kim, S. (2022). A comprehensive review of graph theory applications in transportation networks. Transportation Research Part B: Methodological, 156, 46-68.
 
- Yang, H. and Zhou, J., 1998. Optimal traffic counting locations for origin–destination matrix estimation. Transportation Research Part B: Methodological, 32(2), pp.109-126.
 
- Yang, H., & An, S. (2020). Critical nodes identification in complex networks. Transportation Research Record, 2083(1), 1-12.
 
- Yang, H., Iida, Y. and Sasaki, T., 1991. An analysis of the reliability of an origin-destination trip matrix estimated from traffic counts. Transportation Research Part B: Methodological, 25(5), pp.351-363.
 
- Zaoli, S., Mazzarisi, P., & Lillo, F. (2021) "Betweenness centrality for temporal multiplexes", Scientific Reports, Vol. 11, pp. 4919.
 
- Zhao, S., Zhao, P., & Cui, Y. (2017). A network centrality measure framework for analyzing urban traffic flow: A case study of Wuhan, China. Physica A: Statistical Mechanics and its Applications, 478, 121-128.
Quarterly Journal of Transportation Engineering
Volume 17, Issue 4 - Serial Number 69
Spring 2026
Pages 5685-5708

  • Receive Date 25 July 2025
  • Revise Date 05 January 2026
  • Accept Date 14 February 2026