2.4.2. Matching

Matching reflects the degree of correlation among urban nodes. As the degree of connection among urban nodes is not equivalent, preferential attachment makes the connection among urban nodes correlated. Based on the results of hierarchical calculation, the urban nodes with a large weighted degree tend to "clump" together, which indicates that the network is homogeneous; however, in reality, it is heterogeneous [32]. This is also the case with the homogeneity network relative to the different distribution of the network; it is more easily affected by curing the contact path. Its innovation, low permeability, and external shocks make it difficult to guarantee a quick update and change, leading to increased risk. Hence, the structure's resilience in the matching of urban networks is lower [42]. On this basis, the weighted degree correlation is applied to measure the matching resilience of the structure of the urban network. The formula is as follows [30]:

$$
\overline{NW\_i} = \frac{1}{K\_i} \sum\_{i \in G\_i} \mathcal{W}\_k \qquad \overline{NW\_i} = D \times \mathcal{W}\_k^b \tag{11}
$$

where *NWi* is the neighbor-weighted average degree (NWAD) of city *i*, *Wk* is the weighted degree of neighbor node *k* of city *i*, *Ki* is the degree of city *i*, *Gi* is the set of neighbor nodes of city *i*, *D* is a constant, and *b* is the weighted degree correlation coefficient. Among them, if *b* > 0, it indicates that the network has homogeneity; however, the network has heterogeneity.

## 2.4.3. Transmission

Transmission measures the ability of urban nodes to spread and diffuse in the network through path length, such as the shortest path length [43]. Combined with existing research, this study uses network efficiency to measure the transmission resilience of urban network structures. The formula is [44]:

$$E = \frac{1}{N(N-1)} \sum\_{i \neq j \in G} \frac{1}{D\_{ij}} \tag{12}$$

where *E* is the network efficiency, *Dij* are all the shortest paths from city *i* to city *j*, *N* is the number of nodes in the network, and *G* is the set of the remaining nodes in the network after removing the nodes.
