Neighbor distance centrality
The neighbor distance centrality is a specific case of neighborhood centrality [2], obtained by using degree centrality as the benchmark measure, a decay parameter \(a = 0.2\), and considering neighbors up to two steps (\(n = 2\)) away [3].Formally, for a node \(i\), the neighbor distance centrality is defined as\begin{equation}c_{nd}(i) = d_i + \sum_{j \in \mathcal{N}^{(1)}(i)} (0.2) d_j + + \sum_{j \in \mathcal{N}^{(2)}(i)} (0.2)^2 d_j,\end{equation}where \(d_i\) is the degree centrality of node \(i\) and \(\mathcal{N}^{(k)}(i)\) denotes the set of \(k\)-hop neighbors.The neighbor distance centrality captures the influence of a node by combining its own degree with the degrees of its immediate and secondary neighbors, with contributions decaying with distance. Liu \textit{et al. } [2] reported that this configuration achieves high performance in identifying influential nodes in various network structures.