The mixed core, degree and weighted entropy (MCDWE) method extends MCDE by computing a weighted entropy for each node [2]. For node \(i\), the weighted entropy is
\[
H(i) = \sum_{k=0}^{k_{\max}} \frac{p_k(i) \log_2 p_k(i)}{k_{\max} - |\{r : \exists j \in \mathcal{N}(i), k_s(j) = r\}| + 1},
\]
where \(p_k(i)\) is the fraction of neighbors of node \(i\) in the \(k\)th shell. The centrality of node \(i\) is then
\[
c_{MCDWE}(i) = α k_s(i) + β d_i + γ H(i),
\]
where \(α, β, γ\) are weights controlling the relative contributions of \(k\)-shell, degree, and weighted entropy. Sheikhahmadi and Nematbakhsh [2] suggest \(α = β = γ = 1\). MCDWE emphasizes nodes whose neighbors are spread across shells, refining the ranking of influential nodes.

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] Sheikhahmadi, A., & Nematbakhsh, M. A. (2017). Identification of multi-spreader users in social networks for viral marketing. Journal of Information Science, 43(3), 412-423. doi: 10.1177/0165551516644171.