The extended neighborhood coreness is an extension of the INK score (neighborhood coreness) proposed by Bae et al. [2]. The centrality of node \(i\), denoted by \(c_{nc+}(i)\), is defined as
\begin{equation*}
c_{nc+}(i) = \sum_{j \in \mathcal{N}(i)} c_{INK}(j) = \sum_{j \in \mathcal{N}(i)} \sum_{l \in \mathcal{N}(j)} k_s(l),
\end{equation*}
where \(c_{INK}(i)\) is the INK score of node \(i\), \(k_s(l)\) is the \(k\)-core value of node \(l\), and \(\mathcal{N}(i)\) denotes the set of neighbors of node \(i\).

References

[1] Shvydun, S. (2025). Zoo of Centralities: Encyclopedia of Node Metrics in Complex Networks. arXiv: 2511.05122 https://doi.org/10.48550/arXiv.2511.05122
[2] Bae, J., & Kim, S. (2014). Identifying and ranking influential spreaders in complex networks by neighborhood coreness. Physica A: Statistical Mechanics and its Applications, 395, 549-559. doi: 10.1016/j.physa.2013.10.047.