# Table 1 Definitions for the centrality measures. Let G = (V, E) be an undirected or directed, (strong) connected graph with n = |V| vertices; deg(v) denotes the degree of the vertex v in an undirected graph; dist(v, w) denotes the length of a shortest path between the vertices s and t; σ st denotes the number of shortest paths from s to t and σ st (v) the number of shortest path from s to t that use the vertex v. Let A be the adjacency matrix of the graph G. For a more detailed description and further references please see [8, 27]. Abbreviations used: S.-P.: shortest path, C.-F.: current flow.

Name Definition Remarks Ref
Degree $\mathcal{C}$ deg (v) := deg(v) For directed graphs in- and out-degree is used.
Eccentricity ${\mathcal{C}}_{ℯ\mathcal{c}\mathcal{c}}\left(v\right):=\frac{1}{\mathrm{max}\left\{\text{dist}\left(v,w\right):w\in V\right\}}$   
Closeness ${\mathcal{C}}_{\mathcal{c}\ell ℴ}\left(v\right):=\frac{1}{{\sum }_{w\in V}\text{dist}\left(v,w\right)}$   
Radiality ${\mathcal{C}}_{\mathcal{r}\mathcal{a}\mathcal{d}}\left(v\right):=\frac{{\sum }_{w\in V}\left({\Delta }_{G}+1-\text{dist}\left(v,w\right)\right)}{n-1}$ Δ G is the diameter of the graph G, defined as the maximum distance between any two vertices of G. 
Centroid Value $\mathcal{C}$ cen (v) := min{f(v, w) : w V\{v}} Where f(v, w) := γ v (w) - γ w (v) and γ v (w) denotes the number of vertices that are closer to v than to w. 
Stress $\mathcal{C}$ str (v) :=∑svVtvVδ st (v)   
S.-P. Betweenness $\mathcal{C}$ spb (v) :=∑svVtvVδ st (v) ${\delta }_{st}\left(v\right):=\frac{{\sigma }_{st}\left(v\right)}{{\sigma }_{st}}$ 
C.-F. Closeness ${\mathcal{C}}_{\mathcal{c}\mathcal{f}\mathcal{c}}\left(v\right)=\frac{n-1}{{\sum }_{t\notin v}{p}_{vt}\left(v\right)-{p}_{vt}\left(t\right)}$ Where p vt (t) equals the potential difference in an electrical network. 
C.-F. Betweenness ${\mathcal{C}}_{\mathcal{c}\mathcal{f}\mathcal{b}}\left(v\right)=\frac{1}{\left(n-1\right)\left(n-2\right)}{\sum }_{s,t\in V}{\tau }_{st}\left(v\right)$ Where τ st (v) equals the fraction of electrical current running over vertex v in an electrical network. 
Katz Status ${\mathcal{C}}_{\mathcal{k}\mathcal{a}\mathcal{t}\mathcal{z}}:={\sum }_{k=1}^{\infty }{\alpha }^{k}{\left({A}^{T}\right)}^{k}\stackrel{\to }{1}$ Where α is a positive constant. 
Eigenvector λ$\mathcal{C}$ eiv = A$\mathcal{C}$ eiv The eigenvector to the dominant eigenvalue of A is used. 
Hubbell index $\mathcal{C}$ hbl = $\stackrel{\to }{E}$ + W$\mathcal{C}$ hbl Where $\stackrel{\to }{E}$ is some exogenous input and W is a weight matrix derived from the adjacency matrix A. 
Bargaining $\mathcal{C}$ brg := α(I - βA)-1A$\stackrel{\to }{1}$ Where α is scaling factor and β is the influence parameter. 
PageRank $\mathcal{C}$ pr = dP$\mathcal{C}$ pr + (1 - d)$\stackrel{\to }{1}$ Where P is the transition matrix and d is the damping factor. 
HITS-Hubs $\mathcal{C}$ hubs = A$\mathcal{C}$ auths Assuming $\mathcal{C}$ auths is known. 
HITS-Authorities $\mathcal{C}$ auths = AT$\mathcal{C}$ hubs Assuming $\mathcal{C}$ hubs is known. 
Closeness- vitality $\mathcal{C}$ clv (v) := WI(G) - WI(G\{v}) Where WI(G) is the Wiener index of the graph G. 