**5. Conclusions**

The structural resilience of urban networks is one of the important factors affecting regional sustainable development. Through studying the structural resilience of urban networks in three provinces of Northeast China, the weak links in regional network structures are found, and the network structure is adjusted to promote the rational flow of regional factors, so as to promote the overall high-quality development of the region. To provide relevant references for optimizing the urban network structure resilience at home and abroad, we measured urban network structure resilience and the influencing factors in the three provinces of Northeast China in 2019. This was accomplished through the construction of urban information, transportation, innovation, economy, and integrated networks in the study provinces. As a result, the following conclusions can be drawn:

(1) There are certain similarities among the multi-city networks in the three provinces of Northeast China; nevertheless, there are also major differences. Overall, information, transportation, innovation, economy, and the integrated network show a spatial distribution pattern of "dense in the north and sparse in the south", with closer intra-provincial ties than inter-provincial ties. Nonetheless, the spatial structure differences are evident: The information network shows a multi-core spatial pattern. The main levels have a crossshaped spatial structure in space, which breaks the limitation of regional spatial distance and presents a more complex networked state. The transportation network is evidently affected by geographical spatial proximity, and the flow of transportation elements in neighboring regions is strong. The overall connection of the innovation network is looser, and the connection among urban nodes is relatively weak. The first level of the economic network presents an "N"-shaped structure in Liaoning Province, and the flow of economic factors decreases with increasing spatial distance. The integrated network is more complex than other networks, and the network structure is more robust.

(2) There are evident differences in the resilience characteristics of the multi-city network structure in the three provinces of Northeast China. The information network exhibits the highest heterogeneity, the transmission and agglomeration are at the medium level, and the hierarchy exhibits the lowest. Hence, overall, the information network structure has limited resilience. The hierarchy and heterogeneity of the transportation network are at the medium level, with low transmission and lower agglomeration, and are limited by urban traffic conditions. Hence, the resilience level of the transportation network is low. The innovation network has a high level of hierarchy, with higher transmission, low agglomeration, and the lowest heterogeneity, such that the local network with high resilience has low capability to drive its surrounding network. The economic network has high transmission, agglomeration, higher hierarchy, and low heterogeneity. Hence, its overall resilience is higher. The integrated network is affected by the interaction of multiple networks, and the characteristics of network structure resilience are complicated. Triggering the radiation-driven effect of dominant urban nodes and focusing on the construction and development status of vulnerable urban nodes have important implications for improving the resilience of urban network structures.

(3) The resilience of the multi-city network structure in the three provinces of Northeast China is affected by the interaction of multiple factors. In terms of hierarchy, under the interaction of governmen<sup>t</sup> capacity, political status, urban vitality, and labor wages, the urban network structure demonstrates a phenomenon of heterogeneity. In terms of matching, the urban network structure of the three provinces exhibits high heterogeneity owing to governmen<sup>t</sup> capacity, political status, and urban vitality. In terms of transmission, governmen<sup>t</sup> capacity, political status, and knowledge thickness together shape the transmission resilience of the urban network structure, resulting in a more prominent transmission function of core urban nodes. In terms of agglomeration, governmen<sup>t</sup> capacity, urban vitality, and knowledge thickness are the main factors influencing the agglomeration of the urban network structure; hence, we need to focus on the construction of urban vitality, governmen<sup>t</sup> capacity, and knowledge thickness to enhance the connection among urban nodes.
