Table 2 Description of indicators for network characterization.
From: Spatial correlation network and driving factors of inter-provincial financial risk in China
Indicators | Formula | Description of formulas | |
|---|---|---|---|
Global network | Network density | \(D=\frac{L}{N\times (N-1)}\) | \({\rm{N}}\) is the number of provinces；\({\rm{L}}\) is the number of all relationships present in the financial risk network |
Network hierarchy | \(H=1-\frac{T}{\max (T)}\) | T is the number of provinces with symmetrically reachable points in the financial risk network; max(T) is the number of provinces in the financial risk network | |
Network correlation | \(C=1-\frac{V}{N\times (N-1)/2}\) | N is the number of provinces; V is the number of provinces where the financial risk network is unreachable points | |
Network efficiency | \(E=1-\frac{K}{\max (K)}\) | Kis the total number of redundant association lines present in the financial risk network;\(\max ({\rm{K}})\) is the maximum possible total number of redundant relationships | |
Personal network | Degree of Centrality | \({de}{g}_{i}=\frac{n}{N-1}\) | \({\rm{n}}\) is the total number of associations in the financial risk network |
Proximity centrality | \({cl}{o}_{i}=\frac{\sum _{j}{d}_{{ij}}}{N-1}\) | \({d}_{{ij}}\) is the spherical distance between two provinces in the financial risk network | |
Intermediary Center Degree | \({be}{t}_{i}=\frac{\sum _{j < k}{q}_{{jk}(i)}/{q}_{{jk}}}{(N-1)(N-2)/2}\) | \({q}_{{jk}}\) is the number of optimal paths between province \(i\) and province \(k\), \({q}_{{jk}(i)}\) is the number of province \(i\) through which the optimal path between province\(j\) and province \(k\) passes |
