Link Influence Entropy (LInE) centrality quantifies the importance of each node based on the influence of the links connected to it [2]. The centrality of node \(i\) is determined by the cumulative influence of all links incident to that node:
\[
c_{\mathrm{LInE}}(i) = \sum_{j \in \mathcal{N}(i)} p_{ij},
\]
where \(p_{ij}\) represents the influence of link \((i,j)\), defined according to the change in the average shortest path length after the removal of that link:
\[
p_{ij} = \frac{|\langle d_G \rangle - \langle d_{G_{ij}} \rangle|}{\sum_{i \neq j} |\langle d_G \rangle - \langle d_{G_{ij}} \rangle|}.
\]
Here, \(\langle d_G \rangle\) denotes the average shortest path length in the original graph \(G\), and \(\langle d_{G_{ij}} \rangle\) denotes the corresponding value for the graph obtained by removing link \((i,j)\).
If link \((i,j)\) acts as a bridge (i.e., its removal disconnects the graph), Singh et al. [2] compute \(\langle d_{G_{ij}} \rangle\) using only the largest connected component when it contains more than 80\
If link \((i,j)\) is a bridge (i.e., its removal disconnects the graph), Singh et al. [2] compute \(\langle d_{G_{ij}} \rangle\) using the largest connected component if it contains more than 80\

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] Singh, R., Chakraborty, A., & Manoj, B. S. (2017). GFT centrality: A new node importance measure for complex networks. Physica A: Statistical Mechanics and its Applications, 487, 185-195. doi: 10.1016/j.physa.2017.06.018.