The two-step framework (IF) centrality , also known as the global diversity and local feature (GDLF) method, quantifies node influence using both global and local network information [2, 3]. Global information is derived from the \(k\)-shell decomposition, with entropy used to assess the distribution of a node’s neighbors across shells. Local information is captured by the degree of neighboring nodes. The centrality \( c_{\mathrm{IF}}(i) \) of node \( i \) is defined as\begin{equation*}c_{\mathrm{IF}}(i) = \left(- \sum_{k=1}^{ks_{\max}} p_i(k) \log_2 p_i(k) \right) \left( \log_2 \sum_{j \in \mathcal{N}(i)} d_j \right),\end{equation*}where \begin{equation*}p_i(k) = \frac{x_k(i)}{\sum_{l=1}^{ks_{\max}} x_l(i)}\end{equation*}is the fraction of node \(i\)'s neighbors in the \(k\)-core layer, \( x_k(i) \) is the number of neighbors in the \(k\)-core layer \(k\), \( d_j \) is the degree of neighbor \( j \), and \( \mathcal{N}(i) \) is 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] Fu, Y. H., Huang, C. Y., & Sun, C. T. (2015). Identifying super‐spreader nodes in complex networks. Mathematical Problems in Engineering, 2015(1), 675713. doi: 10.1155/2015/675713.
[3] Fu, Y. H., Huang, C. Y., & Sun, C. T. (2015). Using global diversity and local topology features to identify influential network spreaders. Physica A: Statistical Mechanics and its Applications, 433, 344-355. doi: 10.1016/j.physa.2015.03.042.