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.