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

Applied Network Science

Table 1 Node centrality in weighted networks

Centrality measure	Notation	Definition	Reference
degree	C_D(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)
betweenness	C_B(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)
closeness	C_C(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)

The αω-weighted metrics subsume the ω-weighted metrics (if α=1), which subsume the standard metrics (if ω=1)