Validating urban scaling laws through mobile phone data: analysis of Brazil’s largest cities

Abstract

Urban scaling theories posit that larger cities exhibit disproportionately higher levels of socioeconomic activity and human interactions. Yet, evidence from developing countries (especially those marked by stark socioeconomic disparities) remains limited. To address this gap, we analyse a month-long dataset of 3.1 billion voice-call records from Brazil’s 100 most populous cities, providing a national-scale test of urban scaling laws. We measure interactions using two complementary proxies: the number of phone-based contacts (voice-call degrees) and the number of trips inferred from consecutive calls in distinct locations. Our findings reveal clear superlinear relationships in both metrics, indicating that larger urban centres exhibit intensified remote communication and physical mobility. We further observe that gross domestic product (GDP) also scales superlinearly with population, consistent with broader claims that economic output grows faster than city size. Conversely, the number of antennas required per user scales sublinearly, suggesting economies of scale in telecommunications infrastructure. Although the dataset covers a single provider, its widespread coverage in major cities supports the robustness of the results. We nonetheless discuss potential biases, including city-specific marketing campaigns and predominantly prepaid users, as well as the open question of whether higher interaction drives wealth or vice versa. Overall, this study enriches our understanding of urban scaling especially in the global south, emphasising how communication and mobility jointly shape the socioeconomic landscapes of rapidly growing cities.

Keywords

Urban scaling / CDR data / Human mobility / Social interactions

References

[1] Aguilera A. Business travel and mobile workers. Transportation Research Part A: Policy and Practice. 2008, 42(8): 1109-1116

[2] Ahas R, Aasa A, Silm S, Tiru M. Daily rhythms of suburban commuters’ movements in the tallinn metropolitan area: Case study with mobile positioning data. Transportation Research Part C: Emerging Technologies. 2010, 18(1): 45-54.

[3] Alessandretti L, Natera Orozco LG, Saberi M, Szell M, Battiston F. Multimodal urban mobility and multilayer transport networks. Environment and Planning B: Urban Analytics and City Science. 2023, 50(8): 2038-2070

[4] Alessandretti, L., Sapiezynski, P., Sekara, V. et al. (2018). Evidence for a conserved quantity in human mobility. Nature Human Behaviour, 2 485–491. https://doi.org/10.1038/s41562-018-0364-x

[5] Alexander L, Jiang S, Murga M, González MC. Origin–destination trips by purpose and time of day inferred from mobile phone data. Transportation Research Part C: Emerging Technologies. 2015, 58: 240-250.

[6] Arbesman, S., Kleinberg, J. M., & Strogatz, S. H. (2009). Superlinear scaling for innovation in cities. Physical Review E,79(1), 016115.

[7] Arcaute E, Hatna E, Ferguson P, Youn H, Johansson A, Batty M. Constructing cities, deconstructing scaling laws. Journal of The Royal Society Interface. 2015, 12(102): 20140745.

[8] Arvidsson, M., Lovsjö, N. & Keuschnigg, M. (2023). Urban scaling laws arise from within-city inequalities. Nature Human Behaviour, 7 365–374 (2023). https://doi.org/10.1038/s41562-022-01509-1

[9] Barbosa H, Barthelemy M, Ghoshal G, James CR, Lenormand M, Louail T, Menezes R, Ramasco JJ, Simini F, Tomasini M. Human mobility: Models and applications. Physics Reports. 2018, 734: 1-74.

[10] Barboza, M. H. C., Alencar, R., & de S. Alencar, R., Chaves, J. C., Silva, M. A. H. B., Orrico, R. D., & Evsukoff, A. G. (2021). Identifying human mobility patterns in the rio de janeiro metropolitan area using call detail records. Transportation Research Record,2675(4), 213–221.

[11] Barenblatt, G. I. (1996). Scaling, self-similarity, and intermediate asymptotics. Cambridge University Press.

[12] Barnosky AD, Hadly EA, Bascompte J, Berlow EL, Brown JH, Fortelius M, Getz WM, Harte J, Hastings A, Marquet PA, Martinez ND, Mooers A, Roopnarine P, Vermeij GJ, Williams JW, Gillespie R, Kitzes J, Marshall CR, Matzke N, Mindell DP, Revilla E, Smith AB. Approaching a state shift in earth’s biosphere. Nature. 2012, 486740152-58.

[13] Bathelt H, Malmberg A, Maskell P. Clusters and knowledge: local buzz, global pipelines and the process of knowledge creation. Progress in Human Geography. 2004, 28(1): 31-56.

[14] Bettencourt LM. The origins of scaling in cities. Science. 2013, 340(6139): 1438-1441.

[15] Bettencourt LM, Lobo J, Strumsky D. Invention in the city: Increasing returns to patenting as a scaling function of metropolitan size. Research Policy. 2007, 36(1): 107-120.

[16] Bettencourt LM, Lobo J, West GB. Why are large cities faster? universal scaling and self-similarity in urban organization and dynamics. The European Physical Journal B. 2008, 63(3): 285-293.

[17] Bettencourt LM, Yang VC, Lobo J, Kempes CP, Rybski D, Hamilton MJ. The interpretation of urban scaling analysis in time. Journal of the Royal Society, Interface. 2020, 17(163): 20190846.

[18] Bettencourt LMA. The origins of scaling in cities. Science. 2013, 34061391438-1441.

[19] Bettencourt LMA, Lobo J, Helbing D, Kühnert C, West GB. Growth, innovation, scaling, and the pace of life in cities. Proceedings of the National Academy of Sciences. 2007, 104(17): 7301-7306.

[20] Bettencourt LMA, Samaniego H, Youn H. Professional diversity and the productivity of cities. Scientific Reports. 2014, 4(1): 5393.

[21] Blondel VD, Decuyper A, Krings G. A survey of results on mobile phone datasets analysis. EPJ Data Science. 2015, 4110.

[22] Blondel VD, Decuyper A, Krings G. A survey of results on mobile phone datasets analysis. EPJ Data Science. 2015, 4: 1-55.

[23] Bornstein MH, Bornstein HG. The pace of life. Nature. 1976, 2595544557-559.

[24] Calabrese F, Diao M, Di Lorenzo G, Ferreira J, Ratti C. Understanding individual mobility patterns from urban sensing data: A mobile phone trace example. Transportation Research Part C: Emerging Technologies. 2013, 26: 301-313.

[25] Centers for Disease Control and Prevention. (2012). HIV/AIDS in urban and nonurban areas of the United States. HIV Surveillance Supplemental Report, 17(No. 2). U.S. Department of Health and Human Services.

[26] Chen, Z., & Yeh, A.G.-O. (2022). Delineating functional urban areas in chinese mega city regions using fine-grained population data and cellphone location data: A case of pearl river delta. Computers, Environment and Urban Systems, 93, 101771.

[27] Dong, L., Duarte, F., Duranton, G., Santi, P., Barthelemy, M., Batty, M., Bettencourt, L., Goodchild, M., Hack, G., Liu, Y., Pumain, D., Shi, W., Verbavatz, V., West, G. B., Yeh AG.O., & Ratti, C. (2024). Defining a city–delineating urban areas using cell-phone data. Nature Cities,1(2), 117–125.

[28] Duranton, G., & Puga, D. (2004). Micro-foundations of urban agglomeration economies (vol. 4, pp. 2063–2117). Elsevier Inc.

[29] Duranton G, Puga D. The growth of cities. Handbook of Economic Growth. 2014, 2: 781-853.

[30] Duranton G, Turner MA. Urban growth and transportation. Review of Economic Studies. 2012, 79(4): 1407-1440.

[31] Florida R. Cities and the creative class. City & Community. 2003, 2(1): 3-19.

[32] Fujita M, Krugman P, Mori T. On the evolution of hierarchical urban systems. European Economic Review. 1999, 43(2): 209-251.

[33] Fujita, M., Krugman, P. R., & Venables, A. (2001). The spatial economy: Cities, regions, and international trade. MIT Press.

[34] Garmestani, A. S., Allen, C. R., & Bessey, K. M. (2008). Discontinuities in urban systems: Comparison of regional city-size structure in the united states. In C. Allen & C. Holling (Eds.), Discontinuities in Ecosystems and Other Complex Systems (pp. 136–164). Columbia University Press.

[35] Glaeser, E. L. (2011). The triumph of the city: How our greatest invention makes us richer, smarter, healthier, and happier. The Penguin Press.

[36] Gonzalez MC, Hidalgo CA, Barabasi A-L. Understanding individual human mobility patterns. Nature. 2008, 453(7196): 779-782.

[37] IBGE (2025). Instituto Brasileiro de Geografia e Estatística. censo demográfico 2010: Resultados. https://censo2010.ibge.gov.br/resultados. Accessed 21 Dec 2024.

[38] Isaacman, S., Becker, R., Cáceres, R., Kobourov, S., Martonosi, M., Rowland, J., & Varshavsky, A. (2011). Identifying important places in people’s lives from cellular network data. In Pervasive Computing: 9th International Conference, Pervasive 2011, San Francisco, USA, June 12–15, 2011. Proceedings 9 (pp. 133–151). Springer.

[39] Keuschnigg M. Scaling trajectories of cities. Proceedings of the National Academy of Sciences. 2019, 116(28): 13759-13761.

[40] Keuschnigg, M., Mutgan, S., & Hedström, P. (2019). Urban scaling and the regional divide. Science Advances, 5(1), eaav0042.

[41] Kühnert C, Helbing D, West GB. Scaling laws in urban supply networks. Physica A: Statistical Mechanics and its Applications. 2006, 363(1): 96-103.

[42] Levin, S. A. (1999). Fragile dominion. Perseus Books.

[43] Levin, S. A. & Clark, W. C. (2010). Toward a science of sustainability. Technical report, Center for International Development, Kennedy School of Government, Harvard University.

[44] Lobo, J., Alberti, M., Allen-Dumas, M., Arcaute, E., Barthelemy, M., Bojorquez Tapia, L. A., Brail, S., Bettencourt, L., Beukes, A., Chen, W.-Q., Florida, R., Gonzalez, M., Grimm, N., Hamilton, M., Kempes, C., Kontokosta, C. E., Mellander, C., Neal, Z. P., Ortman, S., ... Youn, H. (2020). Urban science: Integrated theory from the first cities to sustainable metropolises. Technical Report ID 3526940, Social Science Research Network.

[45] Lobo, J., Bettencourt, L. M. A., Strumsky, D., & West, G. B. (2013). Urban scaling and the production function for cities. PLOS ONE,8(3), e58407.

[46] Marquet PA, Quiñones RA, Abades SR, Labra F, Tognelli M, Arim M, Rivadeneira M. Scaling and power-laws in ecological systems. The Journal of Experimental Biology. 2005, 208(9): 1749-1769.

[47] Meirelles, J., Neto, C. R., Ferreira, F. F., Ribeiro, F. L., & Binder, C. R. (2018). Evolution of urban scaling: Evidence from brazil. PLOS ONE,13(10), e0204574.

[48] Milgram, S. (1970). The experience of living in cities: A psychological analysis. In F. F. Korten, S. W. Cook, & J. I. Lacey (Eds.), Psychology and the problems of society (pp. 152–173). American Psychological Association.

[49] Naroll RS, von Bertalanffy L. The principle of allometry in biology and the social sciences. Ekistics. 1973, 36(215): 244-252

[50] Nomaler, O., Frenken, K., & Heimeriks, G. (2014). On scaling of scientific knowledge production in U.S. metropolitan areas. PLOS ONE, 9(10), e110805.

[51] Onnela J-P, Saramäki J, Hyvönen J, Szabó G, Lazer D, Kaski K, Kertész J, Barabási A-L. Structure and tie strengths in mobile communication networks. Proceedings of the National Academy of Sciences. 2007, 104(18): 7332-7336.

[52] Ortman, S. G., Cabaniss, A. H. F., Sturm, J. O., & Bettencourt, L. M. A. (2015). Settlement scaling and increasing returns in an ancient society. Science Advances,1(1), e1400066.

[53] Pan W, Ghoshal G, Krumme C, Cebrian M, Pentland A. Urban characteristics attributable to density-driven tie formation. Nature Communications. 2013, 4(1): 1961.

[54] Pandey B, Brelsford C, Seto KC. Rising infrastructure inequalities accompany urbanization and economic development. Nature Communications. 2025, 1611193.

[55] Prieto-Curiel R, Menezes R. Violence, city size and geographical isolation in african cities. Nature Communications. 2025, 16110049.

[56] Pumain, D. (2004). Scaling laws and urban systems. Santa Fe Institute, Working Paper, (04-02):1–26.

[57] Pumain, D., Paulus, F., Vacchiani-Marcuzzo, C., & Lobo, J. (2006). An evolutionary theory for interpreting urban scaling laws. Cybergeo.

[58] Ribeiro, F., & Netto, V. (2025). Urban scaling laws (1st ed.). Springer Nature.

[59] Ribeiro, F. L., Meirelles, J., Netto, V. M., Neto, C. R., & Baronchelli, A. (2020). On the relation between transversal and longitudinal scaling in cities. PLoS ONE, 1–20.

[60] Ribeiro FL, Rybski D. Mathematical models to explain the origin of urban scaling laws. Physics Reports. 2023, 1012: 1-39.

[61] Ribeiro FL, Zhang P, Gao L, Rybski D. How buildings change the fundamental allometry. Environment and Planning B: Urban Analytics and City Science. 2025, 1: 1-15

[62] Ruiter, J. D., Weston, G., & Lyon, S. M. (2011). Dunbar’s number: Group size and brain physiology in humans reexamined. American Anthropologist,113(4), 557–568.

[63] Samaniego, H., Franco-Cisterna, M., & Sotomayor-Gómez, B. (2020). The topology of communicating across cities of increasing sizes, or the complex task of “reaching out” in larger cities (pp. 97–118). Springer International Publishing.

[64] Schläpfer M, Bettencourt LMA, Grauwin S, Raschke M, Claxton R, Smoreda Z, West GB, Ratti C. The scaling of human interactions with city size. Journal of The Royal Society Interface. 2014, 119820130789.

[65] Sotomayor-Gómez, B., & Samaniego, H. (2020). City limits in the age of smartphones and urban scaling. Computers, Environment and Urban Systems,79, 101423.

[66] Storper M, Venables AJ. Buzz: face-to-face contact and the urban economy. Journal of Economic Geography. 2004, 44351-370.

[67] Toole JL, Colak S, Sturt B, Alexander LP, Evsukoff A, González MC. The path most traveled: Travel demand estimation using big data resources. Transportation Research Part C: Emerging Technologies. 2015, 58: 162-177.

[68] Vanhoof M, Reis F, Ploetz T, Smoreda Z. Assessing the quality of home detection from mobile phone data for official statistics. Journal of Official Statistics. 2018, 34(4): 935-960.

[69] West, G. B. (2017). Scale: The universal laws of growth, innovation, sustainability, and the pace of life in organisms, cities, economies, and companies.

[70] Xu, Z., Xu, G., Lan, T., Li, X., Chen, Z., Cui, H., Zhou, Z., Wang, H., Jiao, L., & Small, C. (2025). Global consistency of urban scaling evidenced by remote sensing. PNAS Nexus, 4(2), pgaf037.

[71] Yuan, Y., Ding, J., Jin, D., & Li, Y. (2025). Learning the complexity of urban mobility with deep generative network. PNAS Nexus, 4(5), pgaf081.

Funding

Fondecyt(1211490)

Chilean national R&D agency (ANID)

Conselho Nacional de Desenvolvimento Científico e Tecnológico(403139/2021-0)

Fundação de Amparo à Pesquisa do Estado de Minas Gerais(APQ-00829-21)

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior(ROR: 00x0ma614)

RIGHTS & PERMISSIONS

The Author(s)