**6. Discussion**

#### *6.1. Optimization Strategies*

With the gradual strengthening of the globalization trend, cities are no longer simple individual units, and the diversified flow of elements connects cities. Hence, it is crucial to maintain a coordinated and stable resilience capacity during the disturbance of the external environment. On this basis, based on the four aspects of hierarchy, matching, transmission, and agglomeration, we propose countermeasures for optimizing the resilience of the urban network structure.

The hierarchy of the urban network structure in the three provinces of Northeast China is evident, and there is a significant trend of heterogeneity, which is significantly influenced by governmen<sup>t</sup> capacity and political status; which results in the prominent core positions of provincial capital cities (Shenyang, Changchun, and Harbin) and sub-provincial cities (Dalian). Therefore, cross-provincial exchanges and cooperation among core cities to realize the linkage development of the three provinces of Northeast China need to be emphasized. In addition, the radiation function of the nodes of core cities should be allowed to drive the development of surrounding areas, realize the synergistic development between core cities and edge cities, promote the flat development of the urban network structure, and enhance the integrity and rationality of the urban network as well as its resistance to the disturbance of the external environment.

Concerning the matching of the urban network structure, enhancing the flow of elements among urban nodes can improve the "robustness" of the linkage paths among nodes and improve the resilience of the urban network structure. Regarding the transportation network, we should improve the construction of the transportation system, focus on strengthening the advantages of national highways, focus on the construction of the "Harbin–Changchun–Shenyang–Dalian" transportation axis, improve the urban transportation conditions, and strengthen the connections among the municipalities in the provinces and among provinces. In terms of the economic network, we must adjust the economic development model, build industrial clusters, promote the development of manufacturing industries, and realize cross-regional economic exchanges and cooperation. The innovation network is affected by regional barriers and has the lowest heterogeneity and resilience. Therefore, it is necessary to eliminate the restrictions of regional conditions, strengthen exchanges between universities and scientific research institutions, cultivate scientific and technological bases, develop regional knowledge bases, and enhance the diversity and flexibility of innovation links among cities.

The transmission and agglomeration of the urban network structure are closely related to the knowledge thickness in the region. In this regard, we should focus on building science and technology centers with regional characteristics, enhancing regional innovation strength, breaking administrative barriers, and strengthening the construction of emergency response plans while promoting the flow of innovation among cities. Furthermore, we should promote the formation of effective two-way links between core city nodes and

other city nodes and enable the radiation-driven role of core urban nodes while enhancing exchanges and interactions among other city nodes to improve and realize an efficiently networked state.

According to the type screening of urban nodes, the dominant urban nodes are essential for influencing the resilience of the urban network structure. When it fails, the resilience of the urban network structure will be seriously damaged; hence, an emergency system of dominant urban nodes should be built to enhance the resilience to cope with external environmental shocks to ensure that urban nodes can operate safely and stably. For vulnerable urban nodes, the construction of public infrastructure should be improved to enhance the resilience of urban nodes to cope with external environmental shocks, and the factor flow between vulnerable urban nodes and other urban nodes should be enhanced to strengthen regional connections.

#### *6.2. Academic Contributions*

The impact of COVID-19 and other uncertainties on cities has had a serious impact on the sustainable development of the region. As a relatively complete and independent economic zone, the three provinces of Northeast China have important material value for the interpretation and clarification of the structural resilience of the entire regional network. In addition, the research can also provide relevant reference for the sustainable development of other similar regions. Therefore, taking regional resilience as the starting point, we introduced multiple data such as the Baidu Index, highway mileage, railway mileage, Web of Science, and other data, and integrated them with traditional statistics to build multiple urban networks based on information, transportation, innovation, and economy for a comprehensive assessment of the structural resilience of urban networks; this, to some degree, avoids the one-sidedness of measuring the resilience of the urban network structure based on single factor flow. In addition, considering that the factor flows among urban nodes are not equal, to reflect the real urban network structure more realistically, weighted network structure resilience is analyzed by giving weights, which enriches and expands the theoretical study of urban networks and resilient regions.

#### *6.3. Potential Bias and Future Steps*

Although this study is valuable in constructing multiple urban connection networks based on multi-source data, it also has some limitations that need to be mitigated by future studies. First, the study only evaluated the resilience of urban networks within 34 cities in the three provinces of Northeast China, without considering the impact of the external environmental factors on the network structure resilience in the study area. Second, due to the limitations of a large amount of data and a time-consuming cleaning process, the study only statically measured the resilience of the urban network structure in 2019. As such, the dynamic evolution characteristics of the resilience of the urban network structure can be analyzed in the future. Finally, because the research on the resilience of the urban network structure is still in the exploratory stage, this study only conducts a preliminary analysis of the factors influencing urban network structure resilience, which needs to be further studied and discussed in the future.

**Author Contributions:** Conceptualization, H.L.; methodology, H.L.; software, H.L.; validation, H.L. and X.L.; formal analysis, H.L.; investigation, H.L.; resources, H.L.; data curation, H.L.; writing— original draft preparation, H.L.; writing—review and editing, S.T. and X.L.; visualization, H.L. and Y.G.; supervision, X.L.; project administration, X.L.; funding acquisition, X.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Natural Science Foundation of China (grant number 41671158).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable. **Data Availability Statement:** The data presented in this study are available on request from the corresponding author.

**Conflicts of Interest:** The authors declare no conflict of interest.
