Table 1 Indicators for evaluating the structure characteristics of spatial correlation network.
Indicators | Equation | Symbolic significance | Function | |
|---|---|---|---|---|
Network density | \(\rho =\frac{2M}{N(N-1)}\) | M and N represent the number of edges and nodes in the network, respectively. | Describes the density of node distribution. | |
Network connectedness | \(C=1-N\times (N-1)/2V\) | C and V represent the connectedness and logarithm of unreachable points in the network, respectively. | Measure the tightness of connections between nodes in the network. | |
Network efficiency | \(E=\frac{1}{N(N-1)}\mathop{\sum}\limits _{i\ne j\in G}\frac{1}{{D}_{ij}}\) | E, Dij, and G represent the efficiency, shortest distance of all from city i to city j, and set of remaining nodes in the network after removing the nodes, respectively | Used to measure the information transfer efficiency in the network. | |
Network hierarchy | \({G}_{H}=1-\frac{V}{MAX(V)}\) | GH, V, and MAX(V) represent the network hierarchy, number of point pairs of mutually symmetrically reachable regions in the correlation network, and maximum number of pairs of points in the network that are mutually reachable by two points, respectively. | Evaluate the stability and complexity of the network. | |
Degree centrality | Out-degree | \({C}_{{\rm{od}}}(i)=\mathop{\sum }\limits_{j=1}^{n}{X}_{ij}/(n-1)\) | X indicates whether there is a direct link between cities, with 1 for a direct link and 0, otherwise. | Measures the number of connections a city has to or by other cities. |
In-degree | \({C}_{{\rm{id}}}(i)=\mathop{\sum }\limits_{j=1}^{n}{X}_{ji}/(n-1)\) | |||
Closeness centrality | Out-closeness centrality | \({C}_{oc}(i)=(n-1)/\mathop{\sum }\limits_{i\ne j,j=1}^{n}d(i,j)\) | d(i,j) represent the shortest distance from a city i to other city j. | Measure the average distance from a node to all other nodes. |
In-closeness centrality | \({C}_{ic}(i)=(n-1)/\mathop{\sum }\limits_{i\ne j,j=1}^{n}d(j,i)\) | |||
Betweenness centrality | \({C}_b({i})=\mathop{\sum}\limits_{{j}{\ne}{i}{\ne}{k}}\frac{{g}_{jk}{(i)}}{{g}_{jk}}\) | gjk and gjk(i) represent the total number of shortest paths between city j and k that generate links and number of shortest paths through city i that generate links from j to k, respectively. | Measure the intermediary role of a node. | |
