| Degree centrality |
\[C_{i}^{D} = \frac{\sum_{j}^{n}e_{ij}}{(n - 1)(n - 2)}\] |
\(C_{i}^{D}\): Degree centrality of node \(i\)
\(e_{ij}\): edge formed by nodes \(i\) and \(j\)
\(n\): total number of nodes |
| Closeness centrality |
\[C_{i}^{C} = \frac{n - 1}{\sum_{i \neq j \in N}^{}d_{ij}}\] |
\(C_{i}^{C}\): Closeness centrality of node \(i\)
\(d_{ij}\): distance from any node \(j\) to node \(i\) |
| Betweenness centrality |
\[C_{i}^{B} = \frac{\sum_{s \neq i \neq t \in N}^{}\frac{\sigma_{st}^{i}}{\sigma_{st}}}{(n - 1)(n - 2)}\] |
\(C_{i}^{B}\): Betweenness centrality of node \(i\)
\(\sigma_{st}\): number of shortest paths between any nodes \(s\) and \(t\)
\(\sigma_{st}^{i}\): number of shortest paths passing through node \(i\) |
| Z-score |
\[Z_{i} = \frac{C_{i} - \mu}{\sigma}\] |
\(Z_{i}\): Standardized centrality of a station \(i\)
\(C_{i}\): Centrality of a station \(i\)
\(\mu\): Average centrality among stations
\(\sigma\): Standard deviation of centrality among stations |
| Pearson coefficient |
\[p_{C,R^{t}}^{t} = \frac{Cov(C,R^{t})}{\sigma_{C}\sigma_{R^{t}}}\] |
\(p_{C,R^{t}}^{t}\): Hourly Pearson correlation coefficient between station centrality (\(C\)) and hourly ridership (\(R^{t}\)), within timeslot t
\(Cov(C,R^{t})\): Covariance of \(C\), \(R^{t}\)
\(\sigma_{C}\), \(\sigma_{R^{t}}\): Standard deviation of \(C\) and \(R^{t}\), respectively |