Special Issues

Advances in modeling spatial interaction network

  • YAN Xiaoyong
  • Institute of Transportation System Science and Engineering, Beijing Jiaotong University, Beijing 100044, China

Received date: 2017-05-12

  Revised date: 2017-06-14

  Online published: 2017-07-29


The spatial interaction network is the space-embedded directed network with flows of people, goods or information among places. Examples of spatial interaction networks include the international trade network, the migration network, the transportation network and the inter-city telecommunication network. Understanding and predicting spatial interaction patterns of these networks are of importance in various disciplines, including the regional science, the transportation science and the economic geography, with many practical applications in the urban or transportation system planning, the epidemiology of infectious diseases, and the location-based services. This paper first introduces briefly two classic spatial interaction models:the gravity model and the intervening opportunity model, and then reviews some recent advances in data-driven spatial interaction models, including the radiation model, the population-weighted opportunity model and the random walk models on spatial interaction networks. This paper also discusses some challenging problems in modeling the spatial interaction networks, such as the individual mobility behavior diversity, the group choice decision behavior experiment and the datadriven modeling approach for the human activity-travel behavior.

Cite this article

YAN Xiaoyong . Advances in modeling spatial interaction network[J]. Science & Technology Review, 2017 , 35(14) : 15 -22 . DOI: 10.3981/j.issn.1000-7857.2017.14.001


[1] Roy J R, Thill J C. Spatial interaction modelling[M]. Berlin:Springer, 2004.
[2] Dejon B. Spatial interaction network flow models[M]. Heidelberg:Physica-Verlag, 1978, 1(1):377-386.
[3] Krings G, Calabrese F, Ratti C, et al. Urban gravity:A model for intercity telecommunication flows[J]. Journal of Statistical Mechanics, 2009, 7:L07003.
[4] Duenas M, Fagiolo G. Modeling the international-trade network:A grav ity approach[J]. Journal of Economic Interaction and Coordination, 2013, 8(1):155-178.
[5] Davis K F, D'Odorico P, Laio F, et al. Global spatio-temporal patterns in human migration:A complex network perspective[J]. PLoS One, 2013, 8(1):e53723.
[6] Kwan M P. Mobile communications, social networks, and urban travel:Hypertext as a new metaphor for conceptualizing spatial interaction[J]. The Professional Geographer, 2007, 59(4):434-446.
[7] Barthélemy M. Spatial networks[J]. Physics Reports, 2011, 499(1):1-101.
[8] 周涛, 韩筱璞, 闫小勇, 等. 人类行为时空特性的统计力学[J]. 电子科技大学学报, 2013, 42(4):482-540. Zhou Tao, Han Xiaopu, Yan Xiaoyong, et al. Statistical mechanics on temporal and spatial activities of human[J]. Journal of University of Electronic Science and Technology of China, 2013, 42(4):482-540.
[9] 邵春福. 交通规划原理[M]. 北京:中国铁道出版社, 2008. Shao Chunfu. Transportation planning theory[M]. Beijing:China Rail way Publishing House, 2008.
[10] de Dios Ortúzar J, Willumsen L G. Modelling transport[M]. Chiches ter:Wiley, 2001.
[11] Desart H G. Théorie des mouvements de voyageurs[M]. Bruxelles:E. Devroye, 1847.
[12] Carey H. Principles of social science[M]. Philadelphia:Lippincott, 1858.
[13] Ravenstein E G. The laws of migration[J]. Journal of the Royal Statisti cal Society, 1885, 48:167-235.
[14] Young E C. The movement of farm population[M]. Cornell University Agricultural Experiment Station, 1924.
[15] Reilly W J. The law of retail gravitation[M]. New York:WJ Reilly, 1931.
[16] Zipf G K. The P1P2/D hypothesis:On the intercity movement of per sons[J]. American Sociological Review, 1946, 11(6):677-686.
[17] Stewart J Q. An inverse distance variation for certain social influences[J]. Science, 1941, 93(2404):89-90.
[18] Kaluza P, Kölzsch A, Gastner M T, et al. The complex network of glob al cargo ship movements[J]. Journal of the Royal Society Interface, 2010, 7(48):1093-1103.
[19] Liu J H, Zhang Z K, Yang C, et al. Gravity effects on information fil tering and network evolving[J]. PLoS ONE, 2014, 9:e91070.
[20] 闫小勇. 一种改进的重力模型标定方法[J]. 交通与计算机, 2003, 21(4):93-95. Yan Xiaoyong. A modified calibration method for gravity model[J]. Transportation and Computer, 2003, 21(4):93-95.
[21] Sheppard E S. Theoretical underpinnings of the gravity hypothesis[J]. Geographical Analysis, 1978, 10(4):386-402.
[22] Wilson A G. A statistical theory of spatial distribution models[J]. Transportation Research, 1967, 1(3):253-269.
[23] Yan X Y, Han X P, Wang B H, et al. Diversity of individual mobility patterns and emergence of aggregated scaling laws[J]. Scientific Re ports, 2013, 3:2678.
[24] Hua C I, Porell F. A critical review of the development of the gravity model[J]. International Regional Science Review, 1979, 4(2):97-126.
[25] Stouffer S A. Intervening opportunities:A theory relating mobility and distance[J]. American Sociological Review, 1940, 5(6):845-867.
[26] 闫小勇. 人类移动模式分析与预测[D]. 北京:北京师范大学系统科学学院, 2014. Yan Xiaoyong. Characterizing and predicting human mobility patterns[D]. Beijing:School of Systems Science, Beijing Normal University, 2014.
[27] Simini F, González M C, Maritan A, et al. A universal model for mo bility and migration patterns[J]. Nature, 2012, 484(7392):96-100.
[28] Offenhuber D, Ratti C. Decoding the city:Urbanism in the age of big data[M]. Berlin:Birkhäuser, 2014.
[29] Yan X Y, Zhao C, Fan Y, et al. Universal predictability of mobility patterns in cities[J]. Journal of the Royal Society Interface, 2014, 11(100):20140834.
[30] Brockmann D, Hufnagel L, Geisel T. The scaling laws of human travel[J]. Nature, 2006, 439(7075):462-465.
[31] González M C, Hidalgo C A, Barabási A L. Understanding individual human mobility patterns[J]. Nature, 2008, 453(7196):779-782.
[32] Song C, Koren T, Wang P, et al. Modelling the scaling properties of human mobility[J]. Nature Physics, 2010, 6(10):818-823.
[33] Belik V, Geisel T, Brockmann D. Natural human mobility patterns and spatial spread of infectious diseases[J]. Physical Review X, 2011, 1(1):011001.
[34] Balcan D, Vespignani A. Phase transitions in contagion processes me diated by recurrent mobility patterns[J]. Nature Physics, 2011, 7(7):581-586.
[35] Camp T, Boleng J, Davies V. A survey of mobility models for ad hoc network research[J]. Wireless Communications and Mobile Computing, 2002, 2(5):483-502.
[36] Bai F, Helmy A. A survey of mobility models[J]. Wireless Adhoc Net works, 2004, 206:1-30.
[37] reactions in fractals and disordered systems[M]. Cambridge:Cam bridge University Press, 2000.
[38] Viswanathan G M, Da Luz M G E,Raposo E P, et al. The physics of foraging:An introduction to random searches and biological encounters[M]. Cambridge:Cambridge University Press, 2011.
[39] Montroll E W, Weiss G H. Random walks on lattices[J]. Journal of Mathematical Physics, 1965, 6(2):167-181.
[40] Hu Y, Zhang J, Huan D, et al. Toward a general understanding of the scaling laws in human and animal mobility[J]. Europhysics Letters, 2011, 96(3):38006.
[41] Han X P, Hao Q, Wang B H, et al. Origin of the scaling law in hu man mobility:Hierarchy of traffic systems[J]. Physical Review E, 2011, 83(3):036117.
[42] Yan X Y, Han X P, Zhou T, et al. Exact solution of the gyration radi us of an individual's trajectory for a simplified human regular mobility model[J]. Chinese Physics Letters, 2011, 28(12):120506.
[43] Szell M, Sinatra R, Petri G, et al. Understanding mobility in a social petri dish[J]. Scientific Reports, 2012, 2:457.
[44] Zhao Y M, Zeng A, Yan X Y, et al. Unified underpinning of human mobility in the real world and cyberspace[J]. New Journal of Physics, 2016, 18:053025.
[45] Zhao Z D, Yang Z, Zhang Z, et al. Emergence of scaling in human-in terest dynamics[J]. Scientific Reports, 2013, 3:3472.
[46] Yan X Y, Wang W X, Gao Z Y, et al. Universal model of individual and population mobility on diverse spatial scales[J]. Working Paper, 2016.
[47] Odlyzko A. The forgotten discovery of gravity models and the ineffi ciency of early railway networks[J]. Oeconomial:History, Methodology, Philosophy, 2015, 5(1):157-192.
[48] Liu Y, Liu X, Gao S, et al. Social sensing:A new approach to under standing our socioeconomic environments[J]. Annals of the Association of American Geographers, 2015, 105(3):512-530.
[49] Lazer D, Pentland A S, Adamic L, et al. Life in the network:The com ing age of computational social science[J]. Science, 2009, 323(5915):721-723.
[50] O'Sullivan D, Manson S M. Do physicists have geography envy? and what can geographers learn from it?[J]. Annals of the Association of American Geographers, 2015, 105(4):704-722.
[51] Pappalardo L, Simini F, Rinzivillo S, et al. Returners and explorers di chotomy in human mobility[J]. Nature Communications, 2015, 6:8166.
[52] Liang X, Zhao J, Xu K. A general law of human mobility[J]. Science China Information Sciences, 2015:58(10):1-14.
[53] Hensher D A, Rose J, Greene B. Applied choice analysis:A primer[M]. Cambridge:Cambridge University Press, 2005.
[54] Mahmassani H S. Learning from interactive experiments:Travel behav ior and complex system dynamics[M]. Bingley:Emerald Publishing, 2009.
[55] Timmermans H, Arentze T, Joh C-H. Analysing space-time behav iour:New approaches to old problems[J]. Progress in Human Geogra phy, 2002, 26(2):175-190.
[56] Buliung R N, Kanaroglou P S. Activity-travel behaviour research:Con ceptual issues, state of the art, and emerging perspectives on behav ioural analysis and simulation modelling[J]. Transport Reviews, 2007, 27(2):151-187.
[57] 张文佳, 柴彦威. 时空制约下的城市居民活动-移动系统——活动分析法的理论和模型进展[J]. 国际城市规划, 2009, 24(4):60-68. Zhang Wenjia, Chai Yanwei. Urban activity-travel systems in the con dition of space-time:A review of activity-based theories and models[J]. Urban Planning International, 2009, 24(4):60-68.
[58] Schneider C M, Belik V, Couronné T, et al. Unravelling daily human mobility motifs[J]. Journal of the Royal Society Interface, 2013, 10(84):20130246.
[59] Widhalm P, Yang Y, Ulm M, et al. Discovering urban activity patterns in cell phone data[J]. Transportation, 2015, 42(4):597-623.
[60] Jiang S, Ferreira Jr J, González M C. Activity-based human mobility patterns inferred from mobile phone data:A case study of Singapore[J]. IEEE Transactions on Big Data, 2015, 12:0163.