From: Structural hole centrality: evaluating social capital through strategic network formation

Measure | Symbol | Formula |
---|---|---|

Shortest-path betweenness centrality | bc | \(c_w = \sum _{u\ne v \ne w}\sum _{\ell } {\mathbb {1}}(m_{\ell uv}>0)f_{\ell uwv}\) |

Shortest-path closeness centrality | cc | \(c_w = \frac{n-1}{\sum _v \ell _{wv}}\) |

Eigenvector centrality | ec | \(c_w = \frac{1}{\lambda _1} \sum _v a_{wv}e_v\) |

Katz centrality | kc | \(c_w = \sum _v \left( ( \text {I} - \delta \text {A}^T)^{\tiny {-1}}-\text {I}\right) _{wv}\) |

Degree centrality | dc | \(c_w = \sum _v a_{wv}\) |

Harmonic centrality | hc | \(c_w = \frac{1}{n-1}\sum _v \frac{1}{\ell _{wv}}\) |

Constraint centrality | conc | \(c_w = \sum _v a_{wv}(p_{wv} + \sum _{u} p_{wu} p_{uv})^2\) |