Exploring the roots of social gravity law

Yan Xiao-Yong

doi:10.7498/aps.69.20191686

Abstract

Many spatial mobility of people, goods and information, such as human travel, population migration, commodity trade, information communication, social interaction and scientific cooperation, follow a law similar to Newton’s law of universal gravitation. This law, named social gravity law, is that the flow between two locations is directly proportional to the product of the vitality of these two locations, and inversely proportional to a power function of their distance. The gravity model established by analogy with the gravity law has also been widely used to predict trip distribution, population migration, interregional trade flows, etc. But why do many complex social systems have such a simple law? It is an interesting and valuable issue. This paper reviews the research on exploring the roots of the social gravity law from various perspectives, including statistical physics, microeconomics, and game theory.

Keywords:

Authors and contacts

Yan Xiao-Yong^1,2

1.
Institute of Transportation System Science and Engineering, Beijing Jiaotong University, Beijing 100044, China
2.
Complex Labortary, University of Electronic Science and Technology of China, Chengdu 611731, China

Corresponding author: Yan Xiao-Yong, yanxy@bjtu.edu.cn

FullText HTML : translate this paragraph

References

[1]	闫小勇 2019 超越引力定律 (北京: 科学出版社) 第iii页 Yan X Y 2019 Beyond Gravity Law (Beijing: China Science Press) piii (in Chinese)
[2]	丁益民, 杨昌平 2012 61 238901 Google Scholar Ding Y M, Yang C P 2012 Acta Phys. Sin. 61 238901 Google Scholar
[3]	Fotheringham A S, O'Kelly M E 1989 Spatial Interaction Models: Formulations and Applications (Dordrecht: Kluwer Academic Publishers) p1
[4]	Sen A, Smith T 1995 Gravity Models of Spatial Interaction Behavior (Berlin: Springer) p1
[5]	Karemera D, Oguledo V I, Davis B 2000 Appl. Econ. 32 1745 Google Scholar
[6]	Porojan A 2001 Open Econ. Rev. 12 265 Google Scholar
[7]	de Dios Ortuzar J, Willumsen L G 2011 Modelling Transport (West Sussex: John Wiley & Sons) p182
[8]	Liu J H, Zhang Z K, Chen L, Liu C, Yang C, Wang X 2014 PloS ONE 9 e91070 Google Scholar
[9]	Ma L L, Ma C, Zhang H F, Wang B H 2015 Physica A 451 205
[10]	Li Z, Ren T, Ma X Q, Liu S M, Zhang Y X, Zhou T 2019 Sci. Rep. 9 8387 Google Scholar
[11]	Newton I 1729 Mathematical Principles of Natural Philosophy (London: Benjamin Motte Publisher) p5
[12]	Dodd S C 1950 Am. Sociol. Rev. 15 245 Google Scholar
[13]	Desart H G 1846 Chemin de fer Direct de Bruxelles vers Gand, par Alost, en Communication avec les Stations Diverses (Bruxelles: Devroye) p16
[14]	Odlyzko A 2015 Economia Hist. Meth. Philos. 5 157
[15]	Carey H C 1858 Principles of Social Science (Philadelphia: Lippincott) p28
[16]	Ravenstein E G 1889 J. R. Stat. Soc. 48 167
[17]	Reilly W J 1929 Methods for the Study of Retail Relationships (Texas: University of Texas Bulletin) p2944
[18]	Zipf G K 1946 Am. Sociol. Rev. 11 677 Google Scholar
[19]	Tobler W 1995 Urban Geogr. 16 327 Google Scholar
[20]	Fagiolo G 2010 J. Econ. Interact. Coor. 5 1 Google Scholar
[21]	周涛, 韩筱璞, 闫小勇, 杨紫陌, 赵志丹, 汪秉宏 2013 电子科技大学学报 42 481 Google Scholar Zhou T, Han X P, Yan X Y, Yang Z M, Zhao Z D, Wang B H 2013 J. Uiv. Electron. Sci. Technol. China 42 481 Google Scholar
[22]	徐赞新, 王钺, 司洪波, 冯振明 2011 60 040501 Google Scholar Xu Z X, Wang Y, Si H B, Feng Z M 2011 Acta Phys. Sin. 60 040501 Google Scholar
[23]	Viboud C, Bjørnstad O N, Smith D L, Simonsen L, Miller M A, Grenfell B T 2006 Science 312 447 Google Scholar
[24]	Jung W S, Wang F, Stanley H E 2008 Europhys. Lett. 81 48005 Google Scholar
[25]	Krings G, Calabrese F, Ratti C, Blondel V D 2009 J. Stat. Mech. 2009 L07003
[26]	Balcan D, Colizza V, Gonçalves B, Hu H, Ramasco J J, Vespignani A 2009 Proc. Natl. Acad. Sci. U.S.A. 106 21484 Google Scholar
[27]	Kaluza P, Kölzsch A, Gastner M T, Blasius B 2010 J. R. Soc. Interface 7 1093 Google Scholar
[28]	Pan R K, Kaski K, Fortunato S 2012 Sci. Rep. 2 902 Google Scholar
[29]	Goh S, Lee K, Park J S, Choi M Y 2012 Phys. Rev. E 86 026102 Google Scholar
[30]	Goh S, Lee K, Choi M Y, Fortin J Y 2014 PloS ONE 9 e89980 Google Scholar
[31]	Levy M, Goldenberg J 2014 Physica A 393 418 Google Scholar
[32]	Sheppard E S 1978 Geogr. Anal. 10 386
[33]	Hua C I, Porell F 1979 Int. Regional Sci. Rev. 4 97 Google Scholar
[34]	Wilson A G 1967 Transp. Res. 1 253 Google Scholar
[35]	Niedercorn J H, Bechdolt Jr B V 1969 J. Regional Sci. 9 273 Google Scholar
[36]	Domencich T A, Mcfadden D 1975 Urban Travel Demand: A Behavioral Analysis (Amsterdam: North-Holland) p1
[37]	Yan X Y, Zhou T 2019 Sci. Rep. 9 9466 Google Scholar
[38]	Pressé S, Ghosh K, Lee J, Dill K A 2013 Rev. Mod. Phys. 85 1115 Google Scholar
[39]	Barthélemy M 2011 Phys. Rep. 499 1 Google Scholar
[40]	Yan X Y, Han X P, Wang B H, Zhou T 2013 Sci. Rep. 3 2678 Google Scholar
[41]	Hensher D A, Button K J 2000 Handbook of Transport Modelling (Oxford: Pergamon) p20
[42]	Chalasani V S, Engebretsen Ø, Denstadli J M, Axhausen K W 2005 J. Transp. Stat. 2 1
[43]	Rietveld P, Zwart B, Van Wee B, van den Hoorn T 1999 Ann. Regional Sci. 33 269 Google Scholar
[44]	Brakman S, Garretsen H 2005 Location and Competition (London: Routledge) p205
[45]	Brockmann D, Hufnagel L, Geisel T 2006 Nature 439 462 Google Scholar
[46]	González M C, Hidalgo C A, Barabási A L 2008 Nature 453 779 Google Scholar
[47]	Han X P, Hao Q, Wang B H, Zhou T 2011 Phys. Rev. E 83 036117 Google Scholar
[48]	Liang X, Zheng X, Lü W, Zhu T, Xu K 2012 Physica A 391 2153
[49]	Gallotti R, Bazzani A, Rambaldi S 2012 Int. J Mod. Phys. C 23 1250061 Google Scholar
[50]	黄飞虎, 彭舰, 由明阳 2016 65 228901 Google Scholar Huang F H, Peng J, You M Y 2016 Acta Phys. Sin. 65 228901 Google Scholar
[51]	Ben-Akiva M E, Lerman S R 1985 Discrete Choice Analysis: Theory and Application to Travel Demand (Cambridge: MIT Press) p1
[52]	McFadden D 2007 Transp. Policy 14 269 Google Scholar
[53]	Herrnstein R J, Loewenstein G F, Prelec D, Vaughan Jr W 1993 Journal of Behav. Decis. Making 6 149 Google Scholar
[54]	Train K E 2009 Discrete Choice Methods with Simulation (Cambridge: Cambridge University Press) p38
[55]	Takemura K 2014 Behavioral Decision Theory: Psychological and Mathematical Descriptions of Human Choice Behavior (Berlin: Springer) p52
[56]	何大韧, 刘宗华, 汪秉宏 2009 复杂系统与复杂网络 (北京: 高等教育出版社) 第59页 He D R, Liu Z H, Wang B H 2009 Complex Systems and Complex Networks (Beijing: Higher Education Press) p59 (in Chinese)
[57]	Rosenthal R W 1973 Int. J Game Theory 2 65 Google Scholar
[58]	Monderer D, Shapley L S 1996 Games Econ. Behav. 14 124 Google Scholar
[59]	Stouffer S A 1940 Am. Sociol. Rev. 5 845 Google Scholar
[60]	Simini F, González M C, Maritan A, Barabási A L 2012 Nature 484 96 Google Scholar
[61]	Yan X Y, Zhao C, Fan Y, Di Z R, Wang W X 2014 J R Soc. Interface 11 20140834 Google Scholar
[62]	Yan X Y, Wang W X, Gao Z Y, Lai Y C 2017 Nat. Commun. 8 1639 Google Scholar
[63]	Voorneveld M, Borm P, Van Megen F, Tijs S, Facchini G 1999 Int. Game Theory Rev. 1 283 Google Scholar
[64]	McFadden D 1980 J. Bus. 1980 S13
[65]	Fisk C 1980 Transp. Res. B 14 243 Google Scholar
[66]	Burgess J 1998 Occam's Razor and Scientific Method (Oxford: Clarendon Press) p195

Cited By

[1]	闫小勇 2019 超越引力定律 (北京: 科学出版社) 第iii页 Yan X Y 2019 Beyond Gravity Law (Beijing: China Science Press) piii (in Chinese)
[2]	丁益民, 杨昌平 2012 61 238901 Google Scholar Ding Y M, Yang C P 2012 Acta Phys. Sin. 61 238901 Google Scholar
[3]	Fotheringham A S, O'Kelly M E 1989 Spatial Interaction Models: Formulations and Applications (Dordrecht: Kluwer Academic Publishers) p1
[4]	Sen A, Smith T 1995 Gravity Models of Spatial Interaction Behavior (Berlin: Springer) p1
[5]	Karemera D, Oguledo V I, Davis B 2000 Appl. Econ. 32 1745 Google Scholar
[6]	Porojan A 2001 Open Econ. Rev. 12 265 Google Scholar
[7]	de Dios Ortuzar J, Willumsen L G 2011 Modelling Transport (West Sussex: John Wiley & Sons) p182
[8]	Liu J H, Zhang Z K, Chen L, Liu C, Yang C, Wang X 2014 PloS ONE 9 e91070 Google Scholar
[9]	Ma L L, Ma C, Zhang H F, Wang B H 2015 Physica A 451 205
[10]	Li Z, Ren T, Ma X Q, Liu S M, Zhang Y X, Zhou T 2019 Sci. Rep. 9 8387 Google Scholar
[11]	Newton I 1729 Mathematical Principles of Natural Philosophy (London: Benjamin Motte Publisher) p5
[12]	Dodd S C 1950 Am. Sociol. Rev. 15 245 Google Scholar
[13]	Desart H G 1846 Chemin de fer Direct de Bruxelles vers Gand, par Alost, en Communication avec les Stations Diverses (Bruxelles: Devroye) p16
[14]	Odlyzko A 2015 Economia Hist. Meth. Philos. 5 157
[15]	Carey H C 1858 Principles of Social Science (Philadelphia: Lippincott) p28
[16]	Ravenstein E G 1889 J. R. Stat. Soc. 48 167
[17]	Reilly W J 1929 Methods for the Study of Retail Relationships (Texas: University of Texas Bulletin) p2944
[18]	Zipf G K 1946 Am. Sociol. Rev. 11 677 Google Scholar
[19]	Tobler W 1995 Urban Geogr. 16 327 Google Scholar
[20]	Fagiolo G 2010 J. Econ. Interact. Coor. 5 1 Google Scholar
[21]	周涛, 韩筱璞, 闫小勇, 杨紫陌, 赵志丹, 汪秉宏 2013 电子科技大学学报 42 481 Google Scholar Zhou T, Han X P, Yan X Y, Yang Z M, Zhao Z D, Wang B H 2013 J. Uiv. Electron. Sci. Technol. China 42 481 Google Scholar
[22]	徐赞新, 王钺, 司洪波, 冯振明 2011 60 040501 Google Scholar Xu Z X, Wang Y, Si H B, Feng Z M 2011 Acta Phys. Sin. 60 040501 Google Scholar
[23]	Viboud C, Bjørnstad O N, Smith D L, Simonsen L, Miller M A, Grenfell B T 2006 Science 312 447 Google Scholar
[24]	Jung W S, Wang F, Stanley H E 2008 Europhys. Lett. 81 48005 Google Scholar
[25]	Krings G, Calabrese F, Ratti C, Blondel V D 2009 J. Stat. Mech. 2009 L07003
[26]	Balcan D, Colizza V, Gonçalves B, Hu H, Ramasco J J, Vespignani A 2009 Proc. Natl. Acad. Sci. U.S.A. 106 21484 Google Scholar
[27]	Kaluza P, Kölzsch A, Gastner M T, Blasius B 2010 J. R. Soc. Interface 7 1093 Google Scholar
[28]	Pan R K, Kaski K, Fortunato S 2012 Sci. Rep. 2 902 Google Scholar
[29]	Goh S, Lee K, Park J S, Choi M Y 2012 Phys. Rev. E 86 026102 Google Scholar
[30]	Goh S, Lee K, Choi M Y, Fortin J Y 2014 PloS ONE 9 e89980 Google Scholar
[31]	Levy M, Goldenberg J 2014 Physica A 393 418 Google Scholar
[32]	Sheppard E S 1978 Geogr. Anal. 10 386
[33]	Hua C I, Porell F 1979 Int. Regional Sci. Rev. 4 97 Google Scholar
[34]	Wilson A G 1967 Transp. Res. 1 253 Google Scholar
[35]	Niedercorn J H, Bechdolt Jr B V 1969 J. Regional Sci. 9 273 Google Scholar
[36]	Domencich T A, Mcfadden D 1975 Urban Travel Demand: A Behavioral Analysis (Amsterdam: North-Holland) p1
[37]	Yan X Y, Zhou T 2019 Sci. Rep. 9 9466 Google Scholar
[38]	Pressé S, Ghosh K, Lee J, Dill K A 2013 Rev. Mod. Phys. 85 1115 Google Scholar
[39]	Barthélemy M 2011 Phys. Rep. 499 1 Google Scholar
[40]	Yan X Y, Han X P, Wang B H, Zhou T 2013 Sci. Rep. 3 2678 Google Scholar
[41]	Hensher D A, Button K J 2000 Handbook of Transport Modelling (Oxford: Pergamon) p20
[42]	Chalasani V S, Engebretsen Ø, Denstadli J M, Axhausen K W 2005 J. Transp. Stat. 2 1
[43]	Rietveld P, Zwart B, Van Wee B, van den Hoorn T 1999 Ann. Regional Sci. 33 269 Google Scholar
[44]	Brakman S, Garretsen H 2005 Location and Competition (London: Routledge) p205
[45]	Brockmann D, Hufnagel L, Geisel T 2006 Nature 439 462 Google Scholar
[46]	González M C, Hidalgo C A, Barabási A L 2008 Nature 453 779 Google Scholar
[47]	Han X P, Hao Q, Wang B H, Zhou T 2011 Phys. Rev. E 83 036117 Google Scholar
[48]	Liang X, Zheng X, Lü W, Zhu T, Xu K 2012 Physica A 391 2153
[49]	Gallotti R, Bazzani A, Rambaldi S 2012 Int. J Mod. Phys. C 23 1250061 Google Scholar
[50]	黄飞虎, 彭舰, 由明阳 2016 65 228901 Google Scholar Huang F H, Peng J, You M Y 2016 Acta Phys. Sin. 65 228901 Google Scholar
[51]	Ben-Akiva M E, Lerman S R 1985 Discrete Choice Analysis: Theory and Application to Travel Demand (Cambridge: MIT Press) p1
[52]	McFadden D 2007 Transp. Policy 14 269 Google Scholar
[53]	Herrnstein R J, Loewenstein G F, Prelec D, Vaughan Jr W 1993 Journal of Behav. Decis. Making 6 149 Google Scholar
[54]	Train K E 2009 Discrete Choice Methods with Simulation (Cambridge: Cambridge University Press) p38
[55]	Takemura K 2014 Behavioral Decision Theory: Psychological and Mathematical Descriptions of Human Choice Behavior (Berlin: Springer) p52
[56]	何大韧, 刘宗华, 汪秉宏 2009 复杂系统与复杂网络 (北京: 高等教育出版社) 第59页 He D R, Liu Z H, Wang B H 2009 Complex Systems and Complex Networks (Beijing: Higher Education Press) p59 (in Chinese)
[57]	Rosenthal R W 1973 Int. J Game Theory 2 65 Google Scholar
[58]	Monderer D, Shapley L S 1996 Games Econ. Behav. 14 124 Google Scholar
[59]	Stouffer S A 1940 Am. Sociol. Rev. 5 845 Google Scholar
[60]	Simini F, González M C, Maritan A, Barabási A L 2012 Nature 484 96 Google Scholar
[61]	Yan X Y, Zhao C, Fan Y, Di Z R, Wang W X 2014 J R Soc. Interface 11 20140834 Google Scholar
[62]	Yan X Y, Wang W X, Gao Z Y, Lai Y C 2017 Nat. Commun. 8 1639 Google Scholar
[63]	Voorneveld M, Borm P, Van Megen F, Tijs S, Facchini G 1999 Int. Game Theory Rev. 1 283 Google Scholar
[64]	McFadden D 1980 J. Bus. 1980 S13
[65]	Fisk C 1980 Transp. Res. B 14 243 Google Scholar
[66]	Burgess J 1998 Occam's Razor and Scientific Method (Oxford: Clarendon Press) p195

[1]	Yang Xiao-Kun, Li Wei, Huang Yong-Chang. Quantum game— “PQ” problem. Acta Physica Sinica, 2024, 73(3): 030301. doi: 10.7498/aps.73.20230592
[2]	Wang Shi-Yuan, Shi Chun-Fen, Qian Guo-Bing, Wang Wan-Li. Prediction of chaotic time series based on the fractional-order maximum correntropy criterion algorithm. Acta Physica Sinica, 2018, 67(1): 018401. doi: 10.7498/aps.67.20171803
[3]	Yang Bo, Fan Min, Liu Wen-Qi, Chen Xiao-Song. Phase transition properties for the spatial public goods game with self-questioning mechanism. Acta Physica Sinica, 2017, 66(19): 196401. doi: 10.7498/aps.66.196401
[4]	Li Yong-Jun, Yin Chao, Yu Hui, Liu Zun. Link prediction in microblog retweet network based on maximum entropy model. Acta Physica Sinica, 2016, 65(2): 020501. doi: 10.7498/aps.65.020501
[5]	Zhang Lei, Yue Hao, Li Mei, Wang Shuai, Mi Xue-Yu. Simulation of pedestrian push-force in evacuation with congestion. Acta Physica Sinica, 2015, 64(6): 060505. doi: 10.7498/aps.64.060505
[6]	Hao Xiao-Chen, Yao Ning, Ru Xiao-Yue, Liu Wei-Jing, Xin Min-Jie. Channel allocation game algorithm based on lifetime model in wireless sensor network. Acta Physica Sinica, 2015, 64(14): 140101. doi: 10.7498/aps.64.140101
[7]	Wang Lu, Ye Shun-Qiang, Xie Neng-Gang. Crossing behavior of pedestrians and vehicles at unsignalized intersection based on dirty faces game. Acta Physica Sinica, 2015, 64(12): 120201. doi: 10.7498/aps.64.120201
[8]	Yang Juan, Yang Dan, Huang Bin, Zhang Xiao-Hong, Yang Cong. Asymptotic stability for non-cooperative program game model of the capacity analysis for mobile ad-hoc networks with variable time delay. Acta Physica Sinica, 2014, 63(2): 020501. doi: 10.7498/aps.63.020501
[9]	Cai Meng, Du Hai-Feng, Marcus W Feldman. A new network structure entropy based on maximum flow. Acta Physica Sinica, 2014, 63(6): 060504. doi: 10.7498/aps.63.060504
[10]	Liu Qun, Yi Jia. The research of the social network evolution based on the evolutionary game theory. Acta Physica Sinica, 2013, 62(23): 238902. doi: 10.7498/aps.62.238902
[11]	Li Yong-Jun, Liu Zun, Yu Hui. Advisor-advisee relationship identification based on maximum entropy model. Acta Physica Sinica, 2013, 62(16): 168902. doi: 10.7498/aps.62.168902
[12]	Wang Can-Jun. Time-delay effect of a stochastic genotype selection model. Acta Physica Sinica, 2012, 61(5): 050501. doi: 10.7498/aps.61.050501
[13]	Wu Yi-Quan, Zhang Jin-Kuang. Image thresholding based on θ-division of 2-D histogram and maximum Shannon entropy. Acta Physica Sinica, 2010, 59(8): 5487-5495. doi: 10.7498/aps.59.5487
[14]	Wei Wei-Feng. Analysis on theory of selective model. Acta Physica Sinica, 2009, 58(11): 7414-7420. doi: 10.7498/aps.58.7414
[15]	Quan Hong-Jun, Wang Bing-Hong, Yang Wei-Song, Wang Wei-Ning, Luo Xiao-Shu. The self-organized segregation effect of evolutionary minority game with imitation. Acta Physica Sinica, 2002, 51(12): 2667-2670. doi: 10.7498/aps.51.2667
[16]	LIU HAI-FENG, ZHAO YAN-YAN, DAI ZHENG-HUA, GONG XIN, YU ZUN-HONG. CALCULATION OF THE LARGEST LYAPUNOV EXPONENT IN THE DISCRETE DYNAMICAL SYSTEM WITH WAVELET ANALYSIS. Acta Physica Sinica, 2001, 50(12): 2311-2317. doi: 10.7498/aps.50.2311
[17]	XU ZU-XIONG, MA RU-ZHANG. MAXIMUM ENTROPY EVALUATION OF OVERLAPPED M?SSBAUER SPECLRA. Acta Physica Sinica, 1988, 37(12): 1949-1955. doi: 10.7498/aps.37.1949
[18]	WEI WEN-DO. MAXIMUM ENTROPY METHOD IN STRUCTURAL ANALYSIS. Acta Physica Sinica, 1986, 35(2): 171-176. doi: 10.7498/aps.35.171
[19]	CHEN SHI-GANG, WANG YOU-QIN. PHENOMENON OF WAVE-LENGTH INCREASE IN RAYLEIGH-BéNARD CONVECTION AND CRITERION OF MAXIMUM ENTROPY PRODUCTION. Acta Physica Sinica, 1983, 32(2): 209-215. doi: 10.7498/aps.32.209
[20]	. . Acta Physica Sinica, 1965, 21(11): 1913-1914. doi: 10.7498/aps.21.1913

Catalog

Vol. 69, Issue 8 - 2020-04-20

Metrics

Abstract views: 10376
PDF Downloads: 300
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板