Extended h -index centrality (EHC) is a node centrality measure that ranks nodes based on the degrees of their neighbors [2]. For each node \(i\), a cumulative function \(CMC(i)\) is first computed as\[CMC(i) = \sum_{k=1}^{h} p^{\,1 + k \frac{p}{r}} \, s_k(i),\]where \(h = \max_j d_j\) is the maximum degree in the network, \(s_k(i)\) is the number of neighbors of node \(i\) with degree greater than or equal to \(k\), and \(p\) and \(r\) are tunable parameters. Experimentally, Zareie and Sheikhahmadi [2] suggest \(p = 0.8\) and \(r = 100\).The extended H-index centrality of node \(i\), denoted \(c_{EHC}(i)\), is then defined as the sum of the cumulative functions of its neighbors:\[c_{EHC}(i) = \sum_{j \in \mathcal{N}(i)} CMC(j).\]

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] Zareie, A., & Sheikhahmadi, A. (2019). EHC: Extended H-index centrality measure for identification of users’ spreading influence in complex networks. Physica A: Statistical Mechanics and its Applications, 514, 141-155. doi: 10.1016/j.physa.2018.09.064.