Neighborhood centrality
The
neighborhood centrality
quantifies the influence of a node by aggregating its own centrality and that of its neighbors up to \( n \) steps away [2]. Let \( f \) denote a benchmark centrality measure. Then, the neighborhood centrality \( c_{nc}(i) \) of node \( i \) is defined as
\begin{equation*}
c_{nc}(i) = f(i) + \sum_{k=1}^n \sum_{j \in \mathcal{N}^{(k)}(i)} a^k f(j),
\end{equation*}
where \( a \in [0,1] \) is a decay parameter and \( \mathcal{N}^{(k)}(i) \) is the set of \( k \)-hop neighbors of node \( i \).
Liu
et al.
[2] considered degree or \(k\)-shell centrality as the benchmark \( f \) and reported the highest performance for neighborhood centrality with \( n = 2 \) and \( a > 0.2 \). When \( f \) is defined as the degree centrality with \( n = 2 \) and \( a = 0.2 \), the measure is referred to as the
neighbor distance centrality
[3].