Local neighbor contribution (LNC) centrality
The
local neighbor contribution
(LNC) centrality quantifies node importance by combining the node’s own structural influence, based on its degree and local neighborhood size, with the aggregated contributions from its nearest and next-nearest neighbors [2]. The local neighbor contribution (LNC) centrality of node \(i\) is defined as
\begin{equation*}
c_{LNC}(i) = O_c(i) \cdot N_c(i),
\end{equation*}
where \(O_c(i)\) represents the node's own structural influence, determined by its degree and the connectivity of its nearest and next-nearest neighbors:
\begin{equation*}
O_c(i) = d_i \cdot |\mathcal{N}^{(\leq 2)}(i)| \sum_{j \in \mathcal{N}^{(\leq 2)}(i)} \frac{1}{d_j} \left(1 - \frac{1}{d_j}\right)^{|\mathcal{N}^{(\leq 2)}(i)|-1},
\end{equation*}
and \(N_c(i)\) represents the contribution from the nearest and next-nearest neighbors of \(i\):
\begin{equation*}
N_c(i) = \frac{|\mathcal{N}^{(\leq 2)}(i)|}{N-1} \sum_{j \in \mathcal{N}(i)} d_j,
\end{equation*}
where \(|\mathcal{N}^{(\leq 2)}(i)|\) denotes the number of nearest and next-nearest neighbors of node \(i\) and \(d_j\) is the degree of node \(j\).