| Network density (D) | Refers to the degree of correlation between network nodes, i.e., the probability of connection between nodes. | $D\text{=}\frac{l}{n\left( n-1 \right)}$ (3) |
| Average path length (L) | Measures the level of network reachability and the average distance between nodes. | $L=\frac{2}{n\left( n-1 \right)}\sum\limits_{i\ne j}{{{d}_{ij}}}$ (4) |
| Average clustering coefficient (C) | Indicates the degree of node aggregation in the network and enables the calculation of the probability that two neighbours of a node may be connected to each other. | $C=\frac{1}{n}\sum\limits_{i\in n}{\frac{2{{m}_{i}}}{{{k}_{i}}\left( {{k}_{i}}-1 \right)}}$ (5) |
| Reciprocity (R) | The ratio of bidirectionally connected edges to all edges in a directed weighted network (Garlaschelli and Loffredo, 2004) and is able to measure the closeness of the interaction between two nodes. | $R=\frac{{{L}_{bi}}}{{{L}_{bi}}+{{L}_{uni}}}$ (6) |
| Degree centrality (DC) | Measures a node’s connectivity and influence, differentiating between its ability to receive and exert influence in directed networks. | $D{{C}_{i}}=\sum\limits_{j=1}^{n}{{{a}_{ji}}{{w}_{ji}}}+\sum\limits_{j=1}^{n}{{{a}_{ij}}{{w}_{ij}}}$ (7) |
| Closeness centrality (CC) | Characterizes the correlation between a city’s development and that of other cities, demonstrates superior efficiency of external interactions in regional development networks. | $C{{C}_{i}}=\frac{n-1}{\sum\nolimits_{j\ne i}^{n}{{{d}^{w}}\left( i,j \right)}}$ (8) |
| Betweenness centrality (BC) | Reflects the ability of cities to play a communicative and coordinating role in regional development, and to control or influence the flow of resources and information. | $B{{C}_{i}}=\frac{2}{(n-1)(n-2)}\sum\limits_{j<k}^{n}{\frac{{{N}_{jk}}\left( i \right)}{{{N}_{jk}}}}$(9) |
| Eigenvector centrality (EC) | Reflects the degree to which the urban entity itself is connected to key nodes in the vicinity (Li et al., 2016), demonstrating the centrality of the nodes | $E{{C}_{i}}={{\lambda }^{-1}}\sum\limits_{j=1}^{n}{{{a}_{ij}}{{x}_{ij}}}$ (10) |
