Malatya centrality is a local centrality measure that evaluates a node's importance relative to the degrees of its neighbors [2]. For a node \(i\), it is defined as
\[
c_{Malatya}(i) = \sum_{j \in \mathcal{N}(i)} \frac{|\mathcal{N}(i)|}{|\mathcal{N}(j)|}=d_i\sum_{j \in \mathcal{N}(i)} \frac{1}{d_j},
\]
where \(\mathcal{N}(i)\) denotes the set of neighbors of nodes \(i\) and \(d_i\) is the degree of node \(i\).
Malatya centrality assigns higher centrality to nodes that have more connections than their neighbors, highlighting nodes that are locally more connected than their immediate surroundings.

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] Öztemiz, F., & Yakut, S. (2024). An Effective Method for Determining Node Dominance Values: Malatya Centrality Algorithm. In 2024 32nd Signal Processing and Communications Applications Conference (SIU) (pp. 1-4). IEEE. doi: 10.1109/SIU61531.2024.10601155.