**1. Introduction**

Resilience originated in the field of ecology, and its primary meaning is the ability of the ecosystem to develop steadily and sustainably [1]. The term "resilience" was gradually applied to other fields such as sociology and psychology [2]. With the continuous acceleration of globalization, industrialization, and urbanization, the disturbance and impact caused by many uncertain factors on urban development are gradually increasing, such that the scale of resilience research has expanded, and resilience is now being explored in urban and regional research. As such, scholars consider theoretical studies and empirical analysis of regional resilience [3–5]; some even believe that a close relationship between urban network structure and regional resilience exists [6,7]. As a new urban geographic system, an urban network constitutes a group of cities in a particular region among which there is a flow of information, material, and energy, thereby making these cities nodes [8]. A typical form of spatial characteristics of resilience is the resilience of the urban network structure; hence, the analysis of the ability of the urban network systems to resist, adapt,

**Citation:** Liu, H.; Li, X.; Tian, S.; Guan, Y. Research on the Evaluation of Resilience and Influencing Factors of the Urban Network Structure in the Three Provinces of Northeast China Based on Multiple Flows. *Buildings* **2022**, *12*, 945. https:// doi.org/10.3390/buildings12070945

Academic Editors: Pierfrancesco De Paola, Francesco Tajani, Marco LocurcioandFelicia DiLiddo

Received: 7 June 2022 Accepted: 30 June 2022 Published: 2 July 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

recover, and maintain their original state under external environmental shocks via inter-city collaboration in ecological, social, economic, and engineering fields is essential [9,10].

A networked urban geographic system is a prerequisite for exploring the resilience of the urban network structure. The spatial organization of cities has changed with the development of an information-based society, and economic globalization has made the relationship among cities increasingly complex. The "space of place" has been replaced by "space of flow," and the urban networks have gradually become a new perspective for studying urban systems [11,12]. Scholars have explored the structural characteristics, evolutionary trends, and influencing factors of urban networks, including enterprise networks [13–15], airline networks [16,17], logistics networks [18], freight networks [19], and information networks [20–22]. Presently, the increasingly complex social environment, urban connectivity, and diverse economic structures have made it essential to enhance the capability of urban networks to cope with shocks for maintaining sustainable regional development [23]. Existing studies have shown that indicators such as network efficiency, diversity, and connectivity can effectively characterize the resilience of urban network structures [24–26]. Unpredictable, uncertain, and frequent natural and man-made disasters can affect urban nodes to a certain extent or can even fail, which can lead to the failure of urban networks and affect the sustainable development of a region [27]. In this regard, building and strengthening the resilience of urban nodes for coping with external environmental shocks has become a key issue that needs to be addressed urgently [28]. Presently, the gradual spread of COVID-19 in the urban network has significantly impacted the healthy development of the region, such that the sudden virus outbreak has reinforced the importance of strengthening the construction of resilient cities and enhancing the structural resilience of urban networks. Meanwhile, the regional cooperation mechanism adopted by China to cope with COVID-19 demonstrates that mutual collaboration among cities in response to external environmental shocks can create a good network synergy [29].

Previous studies provide few empirical results on the resilience of the urban network structure, which still needs to be explored and improved. Meanwhile, most of the existing studies focus on assessing the resilience of the urban network structure and the analysis of optimization strategies, and the discussion on the influence mechanism of urban network structure resilience is insufficient [30]. As the three provinces of Northeast China are located in the center of Northeast Asia and occupy an important strategic position in the development pattern of China, it is significant to analyze the resilience of the urban network structure in the three provinces of Northeast China. In light of this, we take the three provinces as our study area to construct a multi-linkage network through multi-source data and evaluate the characteristics of the resilience of the urban network structure from the four perspectives of hierarchy, matching, transmission, and agglomeration. We explore the influencing factors of urban network structure resilience and propose appropriate optimization strategies as relevant references and theoretical bases for enhancing the resilience of urban networks by adjusting the spatial organization of cities and optimizing the allocation of resources.

#### **2. Research Data and Methods**

#### *2.1. Study Area*

We selected the three provinces of Northeast China as the research area to conduct empirical research. The primary reasons for choosing this area are as follows: (1) As one of the four major economic sectors in China, the regions are connected by the three provinces by relying on the development axis of "Harbin–Changchun–Shenyang–Dalian". As such, affected by geographical proximity and collective rooting, these provinces have close ties with each other. Simultaneously, certain exchanges and cooperation are maintained among them, such that socio-economic ties among the prefectures are characterized by crossover, overlap, and integration, and have strong characteristics of regional integrity. (2) As a complete and independent economic zone, the regional development of the three provinces of Northeast China occupies an important position, and as the window for China's opening

to Northeast Asia, coping with the impact of the external environment in the context of the unstable growth of trade globally, is an important challenge for the urban network structure of the three provinces. Hence, we selected the three provinces of Northeast China as our study area, including Heilongjiang, Jilin, and Liaoning Provinces. Among them, the Daxinganling region of Heilongjiang Province and the Yanbian Korean Autonomous Prefecture of Jilin Province were not included in the research due to missing data. Therefore, a total of 34 prefecture-level cities were considered (Figure 1).

#### *2.2. Data Source*

The data in this article mainly include four parts (Table 1): (1) Baidu Index data, mainly from the official website of Baidu Index search (http://index.baidu.com, accessed on 20–23 June 2021). We used the 34 prefecture-level cities as search keywords to obtain the attention data between two cities at a time in the three provinces from 1 January to 31 December 2019. On this basis, the daily average value was obtained by sorting the data, which was used to characterize the strength of information connection among cities; (2) mileage data, including highway mileage and train and railway mileage, where highway mileage data were searched through the official website of Baidu Map (https: //map.baidu.com, accessed on 26 June 2021) to obtain the highway mileage among 34 cities, and railway mileage data were retrieved based on the railway mileage search website of the train ticket network (http://www.huochepiao.com/licheng/, accessed on 28 June 2021) to obtain the railway mileage between two cities; (3) Paper co-author data, mainly from the Web of Science database (http://webofscience.com, accessed on 3–5 July 2021), were retrieved from the number of co-authored journal papers between two cities in 2019 to characterize the intensity of innovation linkage among cities; (4) statistical data, mainly from Liaoning Province Statistical Yearbook 2020, Jilin Province Statistical Yearbook 2020, and Heilongjiang Province Statistical Yearbook 2020.


**Table 1.** Multi-source data information used in the research.

#### *2.3. Multi-City Network Construction Method*

A prerequisite for exploring the resilience of the urban network structure is the construction of multiple urban networks. In general, regional resilience contains four major domains: ecological, economic, social, and engineering [31–33]. Furthermore, because the research object of this study is the urban network, the ecological domain is considered a substrate of urban construction and development without considering the construction of the corresponding urban network [9]. In addition, cities are the spatial carriers of innovation, such that the innovation cooperation among cities can effectively reflect the regional development capacity [34,35]. Therefore, the innovation domain is considered to be included in the construction of urban networks. To sum up, based on the four domains of economy, society, engineering, and innovation, we constructed the connection network of economy, information, transportation, and innovation. We measured the hierarchy, matching, transmission, and agglomeration of multiple urban network structures. This enabled us to evaluate the resilience of the urban network structure in the three provinces of Northeast China (Figure 2).

**Figure 2.** Multi-city network construction framework.

#### 2.3.1. Information Network

The information connection network among cities is represented in the form of the Baidu Index product between cities, the formula for which is [36]:

$$I = I\_{\vec{ij}} \times I\_{\vec{ji}} \tag{1}$$

where *I* is the information connection strength, *Iij* is the Baidu attention value of city *i* to city *j*, and *Iji* is the Baidu attention value of city *j* to city *i*.

#### 2.3.2. Transportation Network

Considering that roads and railroads are the primary modes of transportation among cities in the three provinces of Northeast China, we constructed the transportation connection network based on the law of gravity with the formula [10]:

$$T = K\_{i\bar{j}} \times \left(\sqrt{P\_i N\_i} \times \sqrt{P\_j N\_{\bar{j}}}\right) / D\_{i\bar{j}}^2 \tag{2}$$

In the formula, *T* is the strength of transportation connection, *Kij* is the gravitational coefficient, which takes the value of 1, *Pi* and *Pj* are the number of economically active populations in city *i* and city *j*, *Ni* and *Nj* are the GDP of city *i* and city *j*, and *Dij* is the sum of the highway and railway mileage between city *i* and city *j*.

#### 2.3.3. Economic Network

Referring to previous research [37], the employed population G in the urban area is chosen to represent the urban functional capacity, and the value of location entropy of a sector's employees in a city determines whether the city has an outward function, and the location entropy Lqij of employees in department *j* in city *i* is presented as follows:

$$\mathbf{L}\mathbf{q}\_{\mathbf{i}\mathbf{j}} = \left(\mathbf{G}\_{\mathbf{i}\mathbf{j}}/\mathbf{G}\_{\mathbf{i}}\right) / \left(\mathbf{G}\_{\mathbf{j}}/\mathbf{G}\right) \text{ (\$i = 1, 2, \dots\$, \$n\$; \$j = 1, 2, \dots\$,\$ m) \tag{3}$$

where, if *Lqij* < 1, the department does not have an export-oriented function and *Eij* = 0. If *Lqij* > 1, the department has an export-oriented function, and, at this time, the exportoriented function *Eij* of department *j* in city *i* is as follows:

$$E\_{i\bar{j}} = G\_{i\bar{j}} - G\_i^\* \left( G\_{\bar{j}} / G \right) \tag{4}$$

Total outward function *Ei* of m departments in city *i:*

$$E\_i = \sum\_{j=1}^{m} E\_{ij} \tag{5}$$

Functional efficiency *Ni* of city *i*:

$$N\_{\dot{l}} = GDP\_{\dot{l}}/G\_{\dot{l}} \tag{6}$$

The amount of outward function impact of city *i*:

$$F\_{\bar{l}} = E\_{\bar{l}} \times N\_{\bar{l}} \tag{7}$$

On this basis, the economic network is constructed based on the gravity model:

$$R = \left(F\_{\mathbf{i}} \times F\_{\mathbf{j}}\right) / D\_{\mathbf{i}\mathbf{j}}^2 \tag{8}$$

where *R* is the strength of economic connection, *Fi* and *Fj* are the amounts of the outward functional influence of city *i* and city *j*, and *Dij* is the linear distance between city *i* and city *j*.

#### 2.3.4. Integrated Network

The TOPSIS method based on the entropy weight method combines the entropy weight method with the TOPSIS method to avoid the influence of subjective weight assignment on analysis structure. Therefore, we chose the entropy weight TOPSIS method to construct the integrated network [38].

#### *2.4. Urban Network Structure Resilience Measure*

Based on relevant research [25,39,40], with the help of the complex network analysis method, the resilience of the urban network structure in the three provinces of Northeast China was assessed from the perspectives of hierarchy, matching, transmission, and agglomeration (Table 2).

**Table 2.** Evaluation indicators of urban network structure resilience.

