Mapping entropy (ME) is a semi-local measure that incorporates both the degree of a node and the degrees of its neighbors [2, 3]. The ME of node \(i\) is defined as
\[
c_{\mathrm{ME}}(i) = - d_i \sum_{j \in \mathcal{N}(i)} \log d_j,
\]
where \(d_i\) is the degree of node \(i\) and \(\mathcal{N}(i)\) denotes the set of neighbors of node \(i\). ME emphasizes nodes with high degree that are connected to neighbors with a wide range of degrees, thus combining node-level and neighborhood-level information.

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.