Mediative effects centrality (MEC)
Mediative effects centrality
(MEC) quantifies the extent to which a node channels or transmits the influence of other nodes, reflecting its mediating role within the network [2]. The MEC score of node \(i\) is defined as
\begin{equation*}
c_{MEC}(i) = \frac{\sum_{k \neq i} \tilde{t}_{(k)i}}{N-1},
\end{equation*}
where \(\tilde{t}_{(k)i}\) quantifies the contribution of node \(i\) in transmitting the impersonal effects of node \(k\):
\begin{equation*}
\tilde{t}_{(k)i} = \frac{\sum_{j \neq i \neq k} t_{(k)ji}}{(N-2) t_{(k)ii}}.
\end{equation*}
Here, \(t_{(k)ji}\) is the \((i,j)\) entry of \(T_{(k)} = (I - W_{(k)})^{-1}\), where \(W_{(k)}\) is the \((N-1) \times (N-1)\) matrix obtained by removing the \(k\)th row and column from the \(N \times N\) row-normalized adjacency matrix \(W\).