Total effects centrality (TEC)
Total effects centrality
(TEC) quantifies the cumulative influence of a node across the network, accounting for the number and length of all paths connecting nodes [2]. The \(N \times N\) matrix of interpersonal effects is computed as
\[
W^{\infty} = \lim_{α \to 1} \big[(I + α W + α^2 W^2 + \dots)(1-α)\big] = \lim_{α \to 1} (I - α W)^{-1} (1-α),
\]
where \(W\) is the \(N \times N\) row-normalized adjacency matrix with self-loops.
The total effect of node \(i\) on other nodes corresponds to column \(i\) of \(W^{\infty}\), and the total effects centrality of node \(i\) is the average of these effects:
\begin{equation*}
c_{TEC}(i) = \frac{\sum_{j \neq i} (W^{\infty})_{ji}}{N-1}.
\end{equation*}
Total effects centrality is closely related to Katz centrality [2], reflecting both direct and indirect influences of a node.