{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,8]],"date-time":"2026-01-08T08:01:58Z","timestamp":1767859318404,"version":"3.49.0"},"reference-count":62,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2023,11,21]],"date-time":"2023-11-21T00:00:00Z","timestamp":1700524800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"China West Normal University Program","award":["23KE006"],"award-info":[{"award-number":["23KE006"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IJGI"],"abstract":"<jats:p>With the deepening of urbanization in China, the coordinated development of cities in different regions is an important part of the sustainable development of the country, and the reasonable quantification of the unbalanced development of cities in different regions is an important issue facing the society nowadays. Previous studies usually use population data to analyze the power-law distribution law to quantify the imbalance of urban development in different regions, but China\u2019s population data span a large number of years and numerous division criteria, and the results obtained from different population data are widely disparate and have obvious limitations. The paper starts from a fractal perspective and utilizes OpenStreetMap (OSM) data to extract national road intersections from 2015 to 2022, calculates critical distance thresholds for eight years using urban expansion curves, generates urban agglomerations in China, and quantifies the imbalance of urban development in different regions by calculating the urban agglomeration power-law index. The results indicate that (1) the critical distance threshold of urban expansion curves exhibits a slight overall increase and stabilizes within the range of 120\u2013130 m, (2) the number of urban agglomerations in China has been increasing significantly year by year, but the power-law index has been decreasing from 1.49 in 2015 to 1.36 in 2022, and (3) the number of urban agglomerations and the power\u2013law index of the Beijing\u2013Tianjin\u2013Hebei, Yangtze River Delta, Pearl River Delta, and Chengdu\u2013Chongqing regions, which is consistent with the national scale trend, indicates that the scale distribution of urban agglomerations in China at this stage does not conform to Zipf\u2019s law, and there is a certain Matthew effect among cities in different geographic areas with a large unevenness. The results of the study can provide new ideas for assessing the coordinated development of cities in different regions. It compensates for the instability of population and economic data in traditional studies.<\/jats:p>","DOI":"10.3390\/ijgi12120472","type":"journal-article","created":{"date-parts":[[2023,11,21]],"date-time":"2023-11-21T12:12:13Z","timestamp":1700568733000},"page":"472","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Assessing Regional Development Balance Based on Zipf\u2019s Law: The Case of Chinese Urban Agglomerations"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2736-4392","authenticated-orcid":false,"given":"Liang","family":"Kong","sequence":"first","affiliation":[{"name":"School of Geographical Science, China West Normal University, Nanchong 637009, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qinglin","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Geographical Science, China West Normal University, Nanchong 637009, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jie","family":"Deng","sequence":"additional","affiliation":[{"name":"School of Geographical Science, China West Normal University, Nanchong 637009, China"},{"name":"Institute of Earth Surface Processes and Environmental Change, China West Normal University, Nanchong 637009, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Leichao","family":"Bai","sequence":"additional","affiliation":[{"name":"School of Geographical Science, China West Normal University, Nanchong 637009, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2954-2244","authenticated-orcid":false,"given":"Zhongsheng","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Geographical Science, China West Normal University, Nanchong 637009, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2491-9033","authenticated-orcid":false,"given":"Zhong","family":"Du","sequence":"additional","affiliation":[{"name":"School of Geographical Science, China West Normal University, Nanchong 637009, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5766-3436","authenticated-orcid":false,"given":"Mingliang","family":"Luo","sequence":"additional","affiliation":[{"name":"School of Geographical Science, China West Normal University, Nanchong 637009, China"},{"name":"Institute of Earth Surface Processes and Environmental Change, China West Normal University, Nanchong 637009, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,11,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1038\/548275a","article-title":"Revitalize the world\u2019s countryside","volume":"548","author":"Liu","year":"2017","journal-title":"Nature"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"103831","DOI":"10.1016\/j.cities.2022.103831","article-title":"Urban expansion and the urban\u2013rural income gap: Empirical evidence from China","volume":"129","author":"Zhong","year":"2022","journal-title":"Cities"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1016\/j.jrurstud.2020.09.005","article-title":"Emerging rural spatial restructuring regimes in China: A tale of three transitional villages in the urban fringe","volume":"93","author":"Zhang","year":"2022","journal-title":"J. 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