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Table 1 Node centrality in weighted networks

From: Detecting social media users based on pedestrian networks and neighborhood attributes: an observational study

Centrality measureNotationDefinitionReference
degreeCD(v)\(\sum \limits _{e_{v}\in E}{a(e_{v})}\)(Diestel 2017)
ω-weighted degree\( C_{D}^{\omega }(v)\)\(\sum \limits _{e_{v}\in E}{\omega (e_{v})}\)(Opsahl et al. 2010)
αω-weighted degree\(C_{D}^{\alpha \omega }(v)\)\(C_{D}(v)^{(1-\alpha)}C_{D}^{\omega }(v)^{\alpha }\,,\alpha >0\)(Opsahl et al. 2010)
betweennessCB(v)\(\sum \limits _{s\neq v\neq t\in V}\frac {\sigma (s,t|v)}{\sigma (s,t)}\)(Freeman 1977)
ω-weighted betweenness\(C_{B}^{\omega }(v)\)\(\sum \limits _{s\neq v\neq t\in V}\frac {\sigma ^{\omega }(s,t|v)}{\sigma ^{\omega }(s,t)}\)(Opsahl et al. 2010)
αω-weighted betweenness\(C_{B}^{\alpha \omega }(v)\)\(\sum \limits _{s\neq v\neq t\in V}\frac {\sigma ^{\alpha \omega }(s,t|v)}{\sigma ^{\alpha \omega }(s,t)}\)(Opsahl et al. 2010)
closenessCC(v)\(\frac {1}{\sum _{t\in V}{\delta (v,t)}}\)(Beauchamp 1965; Sabidussi 1966)
ω-weighted closeness\(C_{C}^{\omega }(v)\)\(\frac {1}{\sum _{t\in V}{\delta ^{\omega }(v,t)}}\)(Opsahl et al. 2010)
αω-weighted closeness\(C_{C}^{\alpha \omega }(v)\)\(\frac {1}{\sum _{t\in V}{\delta ^{\alpha \omega }(v,t)}}\)(Opsahl et al. 2010)
  1. The αω-weighted metrics subsume the ω-weighted metrics (if α=1), which subsume the standard metrics (if ω=1)