Weight degree centrality (WDC, Liu)
The
weight degree centrality
(WDC) quantifies the influence of a node by considering both its own degree and the degrees of its neighbors [2]. The centrality of node \(i\) is defined as
\begin{equation*}
c_{Wdc}(i) = \left( \sum_{j \in \mathcal{N}(i)} d_j - d_i \right) d_i^{α},
\end{equation*}
where \(\mathcal{N}(i)\) denotes the set of neighbors of node \(i\), \(d_i\) is the degree of node \(i\), while \(α\) is a tunable parameter that regulates the contribution of node \(i\)'s degree relative to its neighbors. Liu et al. [2] suggest setting \(α = |r|\), where \(r\) is the degree assortativity coefficient. This allows the centrality measure to adapt to the network type: in
assortative
networks (\(r>0\)), high-degree nodes connecting to other high-degree nodes are emphasized;
in
disassortative
networks (\(r<0\)), high-degree nodes connecting to low-degree nodes are emphasized;
and in
neutral
networks (\(r \approx 0\)), node degrees have uniform influence.