{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,15]],"date-time":"2026-06-15T14:48:20Z","timestamp":1781534900607,"version":"3.54.5"},"reference-count":37,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T00:00:00Z","timestamp":1777507200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["42201229"],"award-info":[{"award-number":["42201229"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["42401212"],"award-info":[{"award-number":["42401212"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"award":["42201229"],"award-info":[{"award-number":["42201229"]}],"id":[{"id":"https:\/\/ror.org\/01h0zpd94","id-type":"ROR","asserted-by":"publisher"}]},{"award":["42401212"],"award-info":[{"award-number":["42401212"]}],"id":[{"id":"https:\/\/ror.org\/01h0zpd94","id-type":"ROR","asserted-by":"publisher"}]},{"name":"the General Project of Ministry of Education Foundation on Humanities and Social Sciences","award":["22YJC790043"],"award-info":[{"award-number":["22YJC790043"]}]},{"DOI":"10.13039\/501100004761","name":"the Natural Science Foundation of Henan Province","doi-asserted-by":"crossref","award":["242300421640"],"award-info":[{"award-number":["242300421640"]}],"id":[{"id":"10.13039\/501100004761","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Systems"],"abstract":"<jats:p>The shift from the central place paradigm to the network paradigm in regional relation research emphasizes the need to elucidate the factors and mechanisms driving urban network dynamics. Leveraging firm-level big data\u2014including a headquarters\u2013branch relationships database (29,359 headquarters and 114,679 branches) and an investment relationships database (21,843 investing firms and 69,733 recipients)\u2014this study constructs an urban network integrating both vertical and horizontal enterprise connections. Using exponential random graph models (ERGMs), it analyzes the influencing factors and driving mechanisms of urban network dynamics in the Yellow River Basin (YRB). This study found that the urban network in the YRB is characterized by multiple isolated \u201ccore\u2013periphery\u201d radial networks. Strong connections are concentrated within each province\u2019s major cities and their immediate surroundings, while horizontal connections across provincial borders are weaker. From 2000 to 2020, the urban network has evolved from isolated \u201ccore\u2013periphery\u201d radial networks to corridor networks where some core nodes are interconnected. The urban network dynamics in the YRB result from the combined influences of the preferential attachment mechanism, the network self-organization mechanism, the multi-dimensional proximity mechanisms, and the geographical boundary effect. Enterprises tend to establish branches or investments in cities with spatial proximity and larger economic scales. Reciprocal and transitive structures significantly facilitate urban network formation. Additionally, institutional proximity, geographical proximity, cultural proximity, cognitive proximity, and geomorphological division all exert varying degrees of influence on enterprise connections between cities.<\/jats:p>","DOI":"10.3390\/systems14050490","type":"journal-article","created":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T06:50:01Z","timestamp":1777618201000},"page":"490","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["How Do Endogenous Structure and Multidimensional Proximity Shape Urban Network Dynamics? Evidence from the Yellow River Basin Using Firm-Level Big Data and ERGMs"],"prefix":"10.3390","volume":"14","author":[{"given":"Shuju","family":"Hu","sequence":"first","affiliation":[{"name":"Key Research Institute of Yellow River Civilization and Sustainable Development, Henan University, Kaifeng 475001, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jinjing","family":"Wan","sequence":"additional","affiliation":[{"name":"Key Research Institute of Yellow River Civilization and Sustainable Development, Henan University, Kaifeng 475001, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jinxiu","family":"Hou","sequence":"additional","affiliation":[{"name":"Key Research Institute of Yellow River Civilization and Sustainable Development, Henan University, Kaifeng 475001, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaohan","family":"Hu","sequence":"additional","affiliation":[{"name":"School of Software, Henan University, Kaifeng 475004, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yongsheng","family":"Sun","sequence":"additional","affiliation":[{"name":"Key Research Institute of Yellow River Civilization and Sustainable Development, Henan University, Kaifeng 475001, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,4,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1925","DOI":"10.1080\/713707232","article-title":"The city network paradigm: Measuring urban network externalities","volume":"37","author":"Capello","year":"2000","journal-title":"Urban Stud."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1111\/j.1467-9663.2007.00394.x","article-title":"From central place to network model: Theory and evidence of a paradigm change","volume":"98","author":"Meijers","year":"2007","journal-title":"Tijdschr. Voor Econ. Soc. Geogr."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"2367","DOI":"10.1080\/00420980220080011","article-title":"Measurement of the world city network","volume":"39","author":"Taylor","year":"2002","journal-title":"Urban Stud."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1016\/j.cities.2005.07.002","article-title":"Banking networks across Brazilian cities: Interlocking cities within and beyond Brazil","volume":"22","author":"Rossi","year":"2005","journal-title":"Cities"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"3018","DOI":"10.1177\/0042098014558541","article-title":"Mapping producer services networks in mainland Chinese cities","volume":"52","author":"Zhao","year":"2015","journal-title":"Urban Stud."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2000","DOI":"10.1177\/0042098017700805","article-title":"Multiple creators of knowledge-intensive service networks: A case study of the Pearl River Delta city-region","volume":"55","author":"Zhang","year":"2018","journal-title":"Urban Stud."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1079","DOI":"10.1080\/00343400701874214","article-title":"Application of the interlocking network model to mega-city-regions: Measuring polycentricity within and beyond city-regions","volume":"42","author":"Taylor","year":"2008","journal-title":"Reg. Stud."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"162","DOI":"10.1080\/00343404.2018.1475728","article-title":"Exploring financial centre networks through inter-urban collaboration in high-end financial transactions in China","volume":"54","author":"Pan","year":"2018","journal-title":"Reg. Stud."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"104680","DOI":"10.1016\/j.cities.2023.104680","article-title":"Predicting the network shift of large urban agglomerations in China using the deep-learning gravity model: A perspective of population migration","volume":"145","author":"Gu","year":"2023","journal-title":"Cities"},{"key":"ref_10","first-page":"343","article-title":"Visualizing the urban network constructed by the most innovative enterprises in China","volume":"9","author":"Ma","year":"2022","journal-title":"Reg. Stud. Reg. Sci."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1016\/j.geoforum.2015.06.006","article-title":"Strategic globalizing centers and sub-network geometries: A social network analysis of multi-scalar energy networks","volume":"64","author":"Martinus","year":"2015","journal-title":"Geoforum"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"102625","DOI":"10.1016\/j.cities.2020.102625","article-title":"Understanding interurban networks from a multiplexity perspective","volume":"99","author":"Hu","year":"2020","journal-title":"Cities"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1016\/j.cities.2016.03.013","article-title":"Urban function connectivity: Characterisation of functional urban streets with social media check-in data","volume":"55","author":"Shen","year":"2016","journal-title":"Cities"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"833","DOI":"10.1111\/grow.12371","article-title":"Evolution of spatial structure patterns of city networks in the Yangtze River Economic Belt from the perspective of corporate pledge linkage","volume":"51","author":"Jin","year":"2020","journal-title":"Growth Change"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"230","DOI":"10.5195\/jwsr.2018.778","article-title":"Review of world city network: A global urban analysis","volume":"24","author":"Timberlake","year":"2018","journal-title":"J. World-Syst. Res."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"3639","DOI":"10.1177\/0042098016685511","article-title":"Mapping urban networks through inter-firm service relationships: The case of China","volume":"54","author":"Pan","year":"2017","journal-title":"Urban Stud."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"725","DOI":"10.1177\/0042098009352362","article-title":"On the economic foundation of the urban network paradigm: Spatial integration, functional integration and economic complementarities within the Dutch Randstad","volume":"47","author":"Burger","year":"2010","journal-title":"Urban Stud."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"751","DOI":"10.1007\/s11067-019-09450-z","article-title":"World city networks shaped by the global financing of Chinese firms: A study based on initial public offerings of Chinese firms on the Hong Kong Stock Exchange, 1999\u20132017","volume":"18","author":"Pan","year":"2018","journal-title":"Netw. Spat. Econ."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"811","DOI":"10.1086\/378930","article-title":"Power and Position in the World City System","volume":"109","author":"Alderson","year":"2004","journal-title":"Am. J. Sociol."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1111\/j.1538-4632.2001.tb00443.x","article-title":"Specification of the world city network","volume":"33","author":"Taylor","year":"2001","journal-title":"Geogr. Anal."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"103005","DOI":"10.1016\/j.cities.2020.103005","article-title":"The evolutionary mechanism of China\u2019s urban network from 1997 to 2015: An analysis of air passenger flows","volume":"109","author":"Zhang","year":"2020","journal-title":"Cities"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"533","DOI":"10.1080\/00343404.2020.1807492","article-title":"Inter-and intra-city networks: How networks are shaping China\u2019s film industry","volume":"55","author":"Wen","year":"2020","journal-title":"Reg. Stud."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"5531","DOI":"10.1109\/ACCESS.2020.3048948","article-title":"The characteristics and modes of urban network evolution in the Yangtze River Delta in China from 1990 to 2017","volume":"9","author":"Zhang","year":"2021","journal-title":"IEEE Access"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1007\/s10290-021-00429-y","article-title":"Modeling complex network patterns in international trade","volume":"158","author":"Herman","year":"2021","journal-title":"Rev. World Econ."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Chakraborty, M., Byshkin, M., and Crestani, F. (2020). Patent citation network analysis: A perspective from descriptive statistics and ERGMs. PLoS ONE, 15.","DOI":"10.1371\/journal.pone.0241797"},{"key":"ref_26","first-page":"845","article-title":"Introduction to network modeling using exponential random graph models (ergm): Theory and an application using R-project","volume":"54","year":"2018","journal-title":"Comput. Econ."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"105869","DOI":"10.1016\/j.cities.2025.105869","article-title":"Understanding the structural evolution and driving mechanisms of urban network using firm-level big data and TERGM modeling","volume":"161","author":"Hu","year":"2025","journal-title":"Cities"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1357","DOI":"10.1111\/grow.12401","article-title":"Characterizing functionally integrated regions in the Central Yangtze River Megaregion from a city-network perspective","volume":"51","author":"Gao","year":"2020","journal-title":"Growth Change"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1080\/0034340052000320887","article-title":"Proximity and Innovation: A Critical Assessment","volume":"39","author":"Boschma","year":"2005","journal-title":"Reg. Stud."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1111\/pirs.12060","article-title":"Regional geographies of intercity corporate networks: The use of exponential random graph models to assess regional network-formation","volume":"94","author":"Liu","year":"2015","journal-title":"Pap. Reg. Sci. Assoc."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"102738","DOI":"10.1016\/j.cities.2020.102738","article-title":"Understanding the structure and determinants of city network through intra-firm service relationships: The case of Guangdong-Hong Kong-Macao Greater Bay Area","volume":"103","author":"Chong","year":"2020","journal-title":"Cities"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"528","DOI":"10.1080\/00343404.2017.1334878","article-title":"Regionalization in the yangtze river delta, China, from the perspective of inter-city daily mobility","volume":"52","author":"Zhang","year":"2017","journal-title":"Reg. Stud."},{"key":"ref_33","first-page":"1041","article-title":"Global city clusters: Theorizing spatial and non-spatial proximity in inter-urban firm networks","volume":"52","author":"Martinus","year":"2017","journal-title":"Reg. Stud."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1969","DOI":"10.1177\/0042098010372685","article-title":"The geography of internet infrastructure: An evolutionary simulation approach based on preferential attachment","volume":"47","author":"Vinciguerra","year":"2010","journal-title":"Urban Stud."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"472","DOI":"10.1177\/01600176211061831","article-title":"Multi-dimensional boundary effects and regional economic integration: Evidence from the Yangtze River Economic Belt","volume":"45","author":"He","year":"2022","journal-title":"Int. Reg. Sci. Rev."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1111\/psj.12118","article-title":"Analyzing policy networks using valued exponential random graph models: Do government-sponsored collaborative groups enhance organizational networks?","volume":"44","author":"Scott","year":"2016","journal-title":"Policy Stud. J."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1270","DOI":"10.1080\/13658816.2018.1563299","article-title":"A network approach to the production of geographic context using exponential random graph models","volume":"33","author":"Radil","year":"2021","journal-title":"Int. J. Geogr. Inf. Sci."}],"container-title":["Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-8954\/14\/5\/490\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T04:12:33Z","timestamp":1777695153000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-8954\/14\/5\/490"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,4,30]]},"references-count":37,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2026,5]]}},"alternative-id":["systems14050490"],"URL":"https:\/\/doi.org\/10.3390\/systems14050490","relation":{},"ISSN":["2079-8954"],"issn-type":[{"value":"2079-8954","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,4,30]]}}}