{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,26]],"date-time":"2025-10-26T14:58:09Z","timestamp":1761490689997,"version":"build-2065373602"},"reference-count":49,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2018,12,27]],"date-time":"2018-12-27T00:00:00Z","timestamp":1545868800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002858","name":"China Postdoctoral Science Foundation","doi-asserted-by":"publisher","award":["197675"],"award-info":[{"award-number":["197675"]}],"id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"Natural Science Foundation of China","doi-asserted-by":"publisher","award":["41701187"],"award-info":[{"award-number":["41701187"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>As complex systems, the spatial structure of urban systems can be analyzed by entropy theory. This paper first calculates the interaction force between cities based on the gravity model, the spatial relationship matrix between cities is constructed using the method of network modeling, and the spatial network modeling of urban system can be calculated. Secondly, the Efficiency Entropy (EE), Quality Entropy (QE), and System Entropy (SE) of urban system network are calculated and analyzed by information entropy. Finally, taking the Huaihe River Basin (HRB) as a case study, model verification and empirical analysis are performed. It is found that the spatio\u2013temporal pattern of the urban system network structure in the basin is uneven: in space, the urban system network in the HRB presents a layer-by-layer spatial distribution centered on the core city of Xuzhou; meanwhile, the overall urban system network in the basin presents an orderly development trend. This study has certain theoretical and practical value for the planning of urban and urban systems and the coordinated development of regions.<\/jats:p>","DOI":"10.3390\/e21010020","type":"journal-article","created":{"date-parts":[[2018,12,27]],"date-time":"2018-12-27T11:29:43Z","timestamp":1545910183000},"page":"20","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Spatio\u2013Temporal Pattern of the Urban System Network in the Huaihe River Basin Based on Entropy Theory"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7208-6753","authenticated-orcid":false,"given":"Yong","family":"Fan","sequence":"first","affiliation":[{"name":"Research Institute for Smart Cities &amp; Shenzhen Key Laboratory of Spatial Information Smart Sensing and Services, School of Architecture and Urban Planning, Shenzhen University, Shenzhen 518061, China"},{"name":"College of Geographic Sciences, Xinyang Normal University, Xinyang 464000, China"}]},{"given":"Renzhong","family":"Guo","sequence":"additional","affiliation":[{"name":"Research Institute for Smart Cities &amp; Shenzhen Key Laboratory of Spatial Information Smart Sensing and Services, School of Architecture and Urban Planning, Shenzhen University, Shenzhen 518061, China"}]},{"given":"Zongyi","family":"He","sequence":"additional","affiliation":[{"name":"School of Resource and Environmental Sciences, Wuhan University, Wuhan 430079, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0189-781X","authenticated-orcid":false,"given":"Minmin","family":"Li","sequence":"additional","affiliation":[{"name":"Research Institute for Smart Cities &amp; Shenzhen Key Laboratory of Spatial Information Smart Sensing and Services, School of Architecture and Urban Planning, Shenzhen University, Shenzhen 518061, China"}]},{"given":"Biao","family":"He","sequence":"additional","affiliation":[{"name":"Research Institute for Smart Cities &amp; Shenzhen Key Laboratory of Spatial Information Smart Sensing and Services, School of Architecture and Urban Planning, Shenzhen University, Shenzhen 518061, China"}]},{"given":"Hao","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Resource and Environmental Sciences, Wuhan University, Wuhan 430079, China"}]},{"given":"Nu","family":"Wen","sequence":"additional","affiliation":[{"name":"Research Institute for Smart Cities &amp; Shenzhen Key Laboratory of Spatial Information Smart Sensing and Services, School of Architecture and Urban Planning, Shenzhen University, Shenzhen 518061, China"}]}],"member":"1968","published-online":{"date-parts":[[2018,12,27]]},"reference":[{"key":"ref_1","unstructured":"Mayhew, S. 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