Classified neighbors centrality is an algorithm for identifying influential spreaders that classifies the neighbors of a node according to their relative order of removal during the \(k\)-shell decomposition [2]. Each neighbor \(j\) of node \(i\) is assigned to one of four groups based on the \(k\)-shell decomposition:


  1. Upper neighbors (\(U_i\)) : \(k\)-shell value of node \(j\) is greater than that of node \(i\).

  2. Equal-upper neighbors (\(EU_i\)) : nodes \(j\) and \(i\) have the same \(k\)-shell value, but node \(j\) is removed later than node \(i\).

  3. Equal-lower neighbors (\(EL_i\)) : nodes \(j\) and \(i\) have the same \(k\)-shell value, but node \(j\) is removed earlier than node \(i\).

  4. Lower neighbors (\(L_i\)) : \(k\)-shell value of node \(j\) is less than that of node \(i\).


The centrality of node \(i\), denoted \(c_{CN}(i)\), is defined as
\[
c_{CN}(i) = α |U_i| + β |EU_i| + γ |EL_i| + μ |L_i|,
\]
where \(α, β, γ, μ \in [0,1]\) are tunable parameters. Li et al. [2] suggest \(α = 0.4\), \(β = 0.35\), \(γ = 0.25\), and \(μ = 0.1\), which correspond to the normalized values \(α = 0.364\), \(β = 0.318\), \(γ = 0.227\), and \(μ = 0.091\).

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] Li, C., Wang, L., Sun, S., & Xia, C. (2018). Identification of influential spreaders based on classified neighbors in real-world complex networks. Applied Mathematics and Computation, 320, 512-523. doi: 10.1016/j.amc.2017.10.001.