Mapping Entropy Betweenness (MEB) extends the concept of mapping entropy by weighting nodes with betweenness centrality instead of degree centrality [2]. The centrality of node \(i\) is defined as
\begin{equation*}
c_{\text{MEB}}(i) = - BC_i \sum_{j \in \mathcal{N}(i)} \log BC_j,
\end{equation*}
where \(BC_i\) is the normalized betweenness centrality of node \(i\), and \(\mathcal{N}(i)\) denotes its set of neighbors. The normalized betweenness centrality is computed as
\begin{equation*}
BC_i = \frac{\sum_{j\neq k \neq i} \frac{σ_{jk}(i)}{σ_{jk}}}{N^2 - 3N + 2},
\end{equation*}
where \(σ_{jk}\) denotes the number of shortest paths from node \(j\) to node \(k\), and \(σ_{jk}(i)\) represents the number of paths that pass through node \(i\).
The MEB centrality highlights nodes with high betweenness that are also connected to other high-betweenness neighbors, emphasizing their key role in facilitating information flow.

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] Gialampoukidis, I., Kalpakis, G., Tsikrika, T., Vrochidis, S., & Kompatsiaris, I. (2016). Key player identification in terrorism-related social media networks using centrality measures. In 2016 European Intelligence and Security Informatics Conference (EISIC) (pp. 112-115). IEEE. doi: 10.1109/EISIC.2016.029.