Hybrid characteristic centrality (HCC)
Hybrid characteristic centrality
(HCC) is a hybrid measure that combines E-shell hierarchy decomposition and extended degree to evaluate node importance in a network [2].
The
extended degree
of node \(i\) is defined as
\begin{equation*}
d^{ex}(i) = δ d_i + (1-δ) \sum_{j \in \mathcal{N}(i)} d_j,
\end{equation*}
where \(d_i\) is the degree of node \(i\), \(\mathcal{N}(i)\) is the set of neighbors of \(i\) and \(δ \in [0,1]\) balances the contribution of \(i\)'s own degree and its neighbors' degrees. Liu et al. [2] set \(δ = 0.5\).
The
E-shell hierarchy decomposition
is a variant of \(k\)-shell decomposition that uses \(d^{ex}(i)\) instead of the standard degree \(d_i\). The HCC of node \(i\) is then defined as
\begin{equation*}
c_{HCC}(i) = \frac{d^{ex}(i)}{\max_j d^{ex}(j)} + \frac{pos(i)}{\max_j pos(j)},
\end{equation*}
where \(pos(i)\) denotes the iteration at which node \(i\) is removed during the E-shell decomposition.
Nodes with high HCC values are not only structurally central according to the E-shell hierarchy but also well-connected to influential neighbors, reflecting both local and global importance.