Extended h-index centrality (EHC)
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:
\[
c_{EHC}(i) = \sum_{j \in \mathcal{N}(i)} CMC(j).
\]