Local entropy (LE) is a semi-local centrality measure that accounts for the degrees of a node's neighbors [2, 3]. The LE of node \(i\) is defined as
\[
c_{\mathrm{LE}}(i) = - \sum_{j \in \mathcal{N}(i)} d_j \log d_j,
\]
where \(d_j\) is the degree of neighbor node \(j\), and \(\mathcal{N}(i)\) denotes the set of neighbors of node \(i\). This measure captures the heterogeneity of the local neighborhood: higher LE values indicate that node \(i\) is connected to neighbors with diverse degrees.

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] Zhang, Q., Li, M., Du, Y., & Deng, Y. (2014). Local structure entropy of complex networks. arXiv preprint arXiv:1412.3910. doi: 10.48550/arXiv.1412.3910.
[3] Nie, T., Guo, Z., Zhao, K., & Lu, Z. M. (2016). Using mapping entropy to identify node centrality in complex networks. Physica A: Statistical Mechanics and its Applications, 453, 290-297. doi: 10.1016/j.physa.2016.02.009.