Correlation between functional properties of the transportation network and the morphological hierarchy of its elements (case study of the Sverdlovsk Oblast)

Various numerical characteristics of topological and metric properties are often used to study the transport networks. The most popular of them is the betweenness centrality. It is used to describe the hierarchical structure of network elements (arcs and vertices). It equals the number of shortest paths that pass through particular element of the network. Thus, it shows the importance of the element for the whole network.
The betweenness centrality parameter was used by various authors as both an analysis tool and an independent object of study. In particular, many experts were interested in how this indicator reflects the real functioning of a transport network, for example, the utilized capacity of its elements. Correlation and regression analysis of the utilized capacity and betweenness centrality for a number of real networks has shown that there is a direct correlation between these values. However, it is not strong enough to be used to predict the utilized capacity of network elements on the basis of their betweenness centrality.
The paper presents the in-depth study of the relationship between the betweenness centrality and the utilized capacity as a part of more general relationship between the morphological and functional properties of transport network. The utilized capacity of network arcs was modeled for the motorway network of the Sverdlovsk Oblast using the gravity model of origin-destination matrix. Different parameters of the gravity model resulted in different loading modes; each of them was analyzed in terms of their relationship with the betweenness centrality.
As a result of modeling and analysis, it was found that the correlation ratio between the betweenness centrality and the utilized capacity depends much on the transport behavior of network users, namely the distance of their trips. If the average trips length is significantly longer than the average arc length, there is a strong correlation between the betweenness centrality and congestion. Otherwise, there is no significant relationship between the betweenness centrality and the utilized capacity of the network.

1. Baburin V.L., Zemtsov S.P., Kidyaeva V.M. Metodika otsenki potentsiala ekonomiko-geograficheskogo polozheniya gorodov Rossii [Methodology of evaluating the potential of the economicgeographical position of Russia’s towns], Vestn. Mosk. un-ta, Ser. 5, Geogr., 2016, no. 1, p. 39–45. (In Russian)

2. Baklanov P.Ya., Moshkov A.V., Romanov M.T. Bazisnye strukturnye zven’ya v dolgosrochnom razvitii transportnykh sistem Dal’nevostochnogo regiona Rossii [Basic structural links in the longterm development of transport systems of the Far Eastern region of Russia], Vestn. Mosk. un-ta, Ser. 5, Geogr., 2018, no. 4, p. 83–92. (In Russian)

3. Barthelemy M. Spatial networks, Physics Reports-review Section of Physics Letters, 2011, no. 1, p. 1–101.

4. Bugromenko V.N. Transport v territorial’nykh sistemakh [Transport in territorial systems], Moscow, Nauka Publ., 1987, 112 p. (In Russian)

5. Evans A.W. The calibration of trip distribution models with exponential or similar cost function, Transportation Research, 1971, vol. 5, p. 15–38, DOI: 10.1016/0041-1647(71)90004-9.

6. Haggett P., Chorley R. Network Analysis in Geography, London, Edward Arnold, 1969, 348 p.

7. Kaluza P., Koelzsch A., Gastner M.T., Blasius B. The complex network of global cargo ship movements, Journal of the Royal Society Interface, 2010, no. 48, p. 1093–1103.

8. Kansky K. Structure of transportation networks: relationships between network geometry and regional characteristics, Chicago, University of Chicago Press, 1969, 155 p.

9. Karpachevskii A.M., Shilyakina M.N. Izuchenie dinamiki struktury kaliningradskoi energosistemy na osnove setevogo analiza [The study of the structure dynamics of the Kaliningrad power system based on the network analysis], Okruzhayushchaya sreda i energovedenie, 2019, no. 2, p. 14–24. (In Russian)

10. Kazerani A., Winter S. Can betweenness centrality explain traffic flow, Proceedings of the 12th AGILE International Conference on Geographic Information Science, Hannover, Leibniz Universitдt Hannover, 2009, 9 p.

11. Kazerani A., Winter S. Modified betweenness centrality for predicting traffic flow. Proceedings of the 10th International Conference on GeoComputation, Sydney, University of New South Wales, 2009, 5 p.

12. Krings G., Calabrese F., Ratti C., Blondel V.D. A gravity model for inter-city telephone communication networks, Journal of Statistical Mechanics: Theory and Experiment, 2009, vol. 2009, p. L07003, DOI: http://dx.doi.org/10.1088/1742-5468/2009/07/L07003.

13. Kurant M., Thiran P. Layered complex networks, Physical Review Letters, 2006, vol. 96(13):138701, DOI: 10.1103/PhysRev Lett.96.138701.

14. Martynenko A.V. Programma Wolfram Mathematica kak universal’naya sreda dlya obrabotki i analiza geograficheskoi informatsii [The Wolfram Mathematica program as a universal tool for processing and analysing geographic information], Geograficheskii vestnik, 2016, no. 4, p. 129–138. (In Russian)

15. Martynenko A.V. Vzaimosvyaz’ funktsional’nykh klassov avtomobil’nykh dorog s pokazatelem tsentral’nosti (na primere avtodorozhnoi seti Sverdlovskoi oblasti) [Relationship between functional classes of motor roads and the centrality factor (case study of motorroad network of the Sverdlovsk Oblast)], Vestnik UrGUPS, 2015, no. 4, p. 9–16. (In Russian)

16. Martynenko A.V., Petrov M.B. Vliyanie nachertaniya transportnoi seti na pokazateli dostupnosti (na primere Sverdlovskoi oblasti) [Influence of surface transportation network on accessibility (by the example of the Sverdlovsk Oblast)], Regional research, 2016, no. 2, p. 21–30. (In Russian)

17. Mateiko O.M., Tanygina A.N. Vysshaya matematika dlya geografov: uchebnoe posobie dlya studentov geograficheskikh i geoekologicheskikh spetsial’nostei vuzov [Higher mathematics for geographers: textbook for students of geographical and geoecological specialties of higher education institutions], Minsk, BGU Publ., 2011, 267 p. (In Russian)

18. Nosyreva E.V. Sravnitel’nyi analiz topologicheskikh svoistv setei elektrosnabzheniya Italii i Vostochnoi Sibiri [Comparative analysis of topological properties of electrical supply networks in Italy and Eastern Siberia], Vestnik IrGTU, 2018, no. 11, p. 170– 181. (In Russian)

19. Ortuzar J.D., Willumsen L.G. Modelling Transport, Chichester, John Wiley & Sons Ltd, 2011, 606 p.

20. Panov R.D. Evolyutsiya prostranstvennoi struktury setei krupneishikh metropolitenov mira [Evolution of spatial structure of the world’s biggest subway networks], Izvestiya RAN, Seriya geograficheskaya, 2020, no. 1, p. 20–26. (In Russian)

21. Puzis R., Altshuler Y., Elovici Y., Bekhor S., Shiftan Y., Pentland A. Augmented Betweenness Centrality for Environmentally Aware Traffic Monitoring in Transportation Networks, Journal of Intelligent Transportation Systems, 2013, vol. 17, p. 91–105, DOI: 10.1080/15472450.2012.716663.

22. Shcherbakova N.G. Mery tsentral’nosti v setyakh [Measures of centrality in networks], Problemy informatiki, 2015, no. 2, p. 18– 30. (In Russian)

23. Shumilov A.V. Otsenivanie gravitatsionnykh modelei mezhdunarodnoi torgovli: obzor osnovnykh podkhodov [Estimating gravity models of international trade: a survey of methods], Ekonomicheskii zhurnal Vysshei shkoly ekonomiki, 2017, no. 2, p. 224–250. (In Russian)

24. Syaolin’ L., Anokhin A.A., Shendrik A.V., Chunlyan S. Izmeneniya v prostranstvennom raspredelenii naseleniya i dorozhnoi seti Sankt-Peterburga [Changes in the spatial distribution of population and transport network of Saint Petersburg], Baltiiskii region, 2016, no. 4, p. 53–77. (In Russian)

25. Tarkhov S.A. Analiz topologicheskikh defektov sukhoputnoi transportnoi seti regionov Sibiri i Dal’nego Vostoka [Analysis of topological defects of land transport network of Siberia and Russian Far East regions], Regional’nye issledovaniya, 2019, no. 3, p. 53–62. (In Russian)

26. Tarkhov S.A. Evolyutsionnaya morfologiya transportnykh setei [Evolutional morphology of transport networks], Smolensk, Universum Publ., 2006, 386 p. (In Russian)

27. Tarkhov S.A. Prostranstvennye zakonomernosti rosta vysokoskorostnykh zheleznykh dorog v mire [Spatial consistency of world widehigh-speed railways’ growth], Regional’nye issledovaniya, 2016, no. 4, p. 90–104. (In Russian)

28. Weiyan L., Xin L., Tao L., Bin L. Approximating betweenness centrality to identify key nodes in a weighted urban complex transportation network, Journal of Advanced Transportation, 2019, Article ID 9024745, 8 p., DOI: 10.1155/2019/9024745.

29. Zin’kina Yu.V., Korotaev A.V., Andreev A.I. Struktura global’noi migratsionnoi seti i dinamika izmeneniya Mir-Sistemy [The structure of global migration network and dynamics changes in the world system], Vestn. Mosk. un-ta, Ser. 27, Globalistika i geopolitika, 2014, no. 1–2, p. 18–32. (In Russian)