Weight neighborhood centrality
The
weight neighborhood centrality
quantifies the influence of a node by combining its own centrality with the weighted centralities of its neighbors [2]. Let \( f \) denote a benchmark centrality measure. Then, the weight neighborhood centrality \( c_{wnc}(i) \) of node \( i \) is defined as
\begin{equation*}
c_{wnc}(i) = f(i) + \sum_{j \in \mathcal{N}(i)} \frac{w_{ij}}{\overline{w}} f(j),
\end{equation*}
where \( w_{ij} = (d_i d_j)^{α} \), \( d_i \) and \( d_j \) are the degrees of nodes \( i \) and \( j \),
\( α \) is a tunable parameter, and \( \overline{w} \) is the average importance of all links in the network. Wang et al. [2] used \( α = 1 \) and considered degree or \(k\)-shell centrality as the benchmark \( f \).