The mixed core, semi-local degree, and entropy (MCSDE) method [2] is a variant of MCDE that replaces the standard degree \(d_i\) with the LocalRank (semi-local) centrality. For node \(i\), the centrality is defined as\[c_{MCSDE}(i) = α k_s(i) + β \ c_{\mathrm{LR}}(i) + γ H(i),\]where \(k_s(i)\) is the \(k\)-shell index, \(c_{\mathrm{LR}}(i)\) is the LocalRank centrality of node \(i\), which is defined in [3], \(α, β, γ\) are weights controlling the contributions of each component (Sheikhahmadi and Nematbakhsh [2] suggest \(α = β = γ = 1\)), and \(H(i)\) is the entropy of node \(i\):\[H(i) = \sum_{k=0}^{k_{\max}} p_k(i) \log_2 p_k(i),\]with \(k_{\max}\) being the maximum \(k\)-shell index in the network and \(p_k(i)\) denoting the fraction of neighbors of node \(i\) in the \(k\)th shell. MCSDE integrates semi-local neighborhood information with hierarchical node structure, improving the identification of nodes that are critical for spreading processes and network connectivity.

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.
[3] Chen, D., Lü, L., Shang, M. S., Zhang, Y. C., & Zhou, T. (2012). Identifying influential nodes in complex networks. Physica a: Statistical mechanics and its applications, 391(4), 1777-1787. doi: 10.1016/j.physa.2011.09.017.