The effect of “space-time compression” brought about by “space of flow” breaks the traditional logic of resource allocation, reconstructs regional relations and drives the formation of network organization form of regional integration. Metropolitan area is an important spatial form of urbanization, and metropolitan area integration is also an important form of regional integration. It is a theoretical problem to be studied urgently that constructs the theoretical framework of metropolitan area integration to explore the characteristics, effects and mechanism, under the background of “flow space” and network. This study initially constructs a theoretical model of the integrated symbiotic network system of metropolitan areas and looks forward to the future research direction of the integration of metropolitan areas. The research believes that: (1) The integrated symbiotic network system of metropolitan area includes a multi-domain physical facility network and a virtual relationship network, such as economic space, social and cultural space, and ecological space. It has the dual attributes of symbiotic system and complex network, and reflects the organizational mechanism, evolution direction and law of the metropolitan area integration. (2) The formation mechanism of symbiotic network, the benefit generation mechanism of symbiosis network and the evolution mechanism of symbiosis network system are the basic operation mechanism of the integrated symbiosis network system, reflecting the inherent inevitable connection of metropolitan area integration. (3) The summary of the network characteristics of metropolitan area integration, the comprehensive review of positive and negative effects, the analysis of endogenous, exogenous and network-driven mechanisms at different stages, and the discussion of cross-border and network relationship governance paths, etc. are all important contents for further research on metropolitan area integration. Through the exploration of the theoretical framework construction of metropolitan area integration, it is expected to promote the expansion of research perspective of urban geography and the enrichment of the content, and to provide theoretical guidance in the practice process of the governance and regulation of metropolitan area integrated.

In the context of economic globalization and regional integration, urban development forces have shifted from geographical agglomeration to external network coordination. The connectivity among cities or city network is increasingly becoming “the second essence of cities”. With bibliometric analysis of urban network externality studies, we find that spatial econometric models have been increasingly employed to quantify whether, and to what extent, urban network externality matters in the developmental process of cities or regions. This study first investigated the mathematical properties of spatial econometric models and in particular, the correspondence of model parameters and various measures of urban network externality. More importantly, we highlighted two essential issues of classic spatial econometric models when being applied to model urban network externality: the asymmetric effect and scale effect of urban network externality. Then, we developed an asymmetric spatial economic model (ASEM) to capture the asymmetric effect of urban network externality and, a hierarchical spatial autoregressive model (HSAR) to deal with the scale effect of urban network externality. A series of Monte Carlo simulation experiments were conducted to assess the benefits of these two proposed methodologies. We found that: (1) Ignoring the potential asymmetric effects in the urban network will significantly reduce the accuracy of model parameter estimation. On the other hand, the proposed ASEM can accurately identify the asymmetric effects of network externalities and yield more accurate parameter estimation. (2) Ignoring multi-scale network effects in real world data and modeling the network effects at a single scale will cause serious estimation distortion. The HSAR model instead can provide a reliable quantitative method for modeling the externalities of multi-scale networks.

Networking of the relation among cities is a momentous trend in the development of urban system structure. The connection between cities is often the superposition of multiple elements rather than a single dimension. The urban system of the spatial network of different factor flows differs from each other in spatial organization. Furthermore, the network based on one single factor has obvious limitations so that it is necessary to make a comparative study on the differences of factor flows under the multi-city network. Therefore, this paper, on the basis of four element networks, which are enterprise connection, scientific research cooperation, population migration and gravity simulation, analyzes respectively the external spatial characteristics and disparities of China's urban networks under the perspective of multiple flow space, to be specific, urban node, path connection, community characteristics and etc; explores the internal pattern and law of inter-city connections; as well as attempts to advance proposals to optimize the development of China's urban system. The results reveal that: (1) The spatial organization of multi-city networks shows that the characteristic of similar stability with a “diamond+cross” spatial structure and a “core-node-edge” hierarchical structure, integrates with the characteristic of multiple diversity from the perspective of multi-dimensional data sources; (2) Mobility of population, circulation of materials and other networks that depended on the operation of infrastructure, to some certain extent, are greatly constrained by geographical distance and at the same time show obvious small group characteristics in adjacent areas and strong community structure. However, the less substantial elements such as capital flow and information flow break through this geographical restriction. The focus of the connection lies in the attraction of the target city to the element flow, and the community structure of this type appears to be weak. (3) At present, China's urban connection has the dual characteristics of hierarchy and flattening in form. Therefore, this paper proposes an urban connection model of the “community buzzer-gatekeeper-regional pipeline” model, compatible with the dual features of vertical structure and network structure, applying well for demonstrating the characteristics of China's urban connection, identifying 10 core gatekeeper cities and 8 types of regions in China. Among them, the goalkeeper city with special resources and regional advantages is the leader of the region, playing a key role in undertaking, transforming and spreading various resource elements. This paper aims to improve the theory of urban network and provide theoretical support for urban network development.

Based on extensive data collected from 2000 to 2020 from enterprise headquarters and branches across the whole industry, this paper integrates social network analysis, multi-dimensional proximity analysis, and spatial analysis methods to reveal the spatial pattern, spatio-temporal evolution, and influencing factors of the network of three urban agglomerations in the Yellow River Basin in four aspects: urban node type, hierarchical association, network community division, and their influencing factors. There are five deductions: (1) There is a significant spatial polarization of urban network node intensity that exhibits hierarchical traits. With a greater proportion of first-tier and second-tier cities, the Shandong Peninsula Urban Agglomeration has the most developed network structure. The Central Plains Urban Agglomeration is dominated by second-tier and third-tier cities, while Guanzhong Plain Urban Agglomeration has a high proportion of third-tier and fourth-tier cities. (2) The degree of network association is gradually raised, and the axis level of the urban network is significant. The network, strong in the east and weak in the west, forms a radiation skeleton in the form of a star, focused on Xi'an, Zhengzhou, Jinan, and Qingdao. Horizontal cross-border links among Shandong Peninsula Urban Agglomeration, Central Plains Urban Agglomeration and Guanzhong Plain Agglomeration are lacking. (3) According to the values of degree centrality and betweenness centrality, urban nodes are divided into four types: high degree centrality-high betweenness centrality, low degree centrality-high betweenness centrality, low degree centrality-low betweenness centrality, and high degree centrality-low betweenness centrality. Among them, Qingdao, Jinan, Zhengzhou and Xi'an belong to “high degree centrality-high betweenness centrality” cities in the past 20 years, which are the “hub” and “bridge” of the urban network. (4) Urban network communities are influenced by boundary barrier effect, neighborhood effect and spillover effect. The overall community structure of “three large communities and one small community” and the trend of “clustering first, then merging” has been formed. (5) The evolution and growth of urban networks are positively influenced by geographic proximity, institutional proximity, social proximity, but frequently industrial proximity has a detrimental effect.

Traffic flows is the core factor reflecting the interaction in urban agglomerations and a new measure model of spatial structure. The advanced stage of urban agglomeration is spatial development model of network. The study of spatial signs and interaction mechanism in urban agglomeration from the perspective of network has a reference significance for regional planning and development. In this context, the theory of flow space, social network and pan-maps are applied. Based on Autonavi navigation OD data in the Guangdong-Hong Kong-Macao Greater Bay Area collected in 2019 and 2020, this study constructs a transportation network model and uses a social network analysis approach to analyze its characteristics of spatial construction, node and edge. The conclusions are drawn as follows: After unifying the spatial scale, the Greater Bay Area presents the spatial organization form of “four groups and three circles”; A multi-center networked spatial structure in the Greater Bay Area has been formed relying on core nodes of Dongguan, Shenzhen and Guangzhou; Close local connection and loose overall connection is main characteristics of the network in the Greater Bay Area; There are two strong connection subnetworks in the network: Shenzhen-Dongguan and Guangzhou-Foshan; A continuous thread of connection has not yet formed within the Greater Bay Area. This study reveals the interaction relationship and structural characteristics among regional cities, which is of great significance for promoting the Greater Bay Area to build a multi-polar, group-based and collaborative development pattern. The Greater Bay Area should promote regional cooperation relying on the spatial organization structure and form three major development subgroups: Guangzhou-Foshan-Zhaoqing, Zhuhai-Zhongshan-Jiangmen-Macao and Shenzhen-Dongguan-Huizhou-Hong Kong. Meanwhile, it is necessary for the Greater Bay Area to give play to the advantages of central nodes, deepen the contact of Guangdong-Hong Kong-Macao and enhance international influence relying on transportation strategy and construction of free trade zones.