Clustered local-degree (CLD)
The
clustered local-degree (CLD) centrality
integrates both the degree of neighboring nodes and the local topological structure surrounding each node. In this measure, the local clustering coefficient of a node quantifies the connectivity among its neighbors [2].
The centrality value \( c_{\mathrm{CLD}}(i) \) for node \( i \) is defined as
\begin{equation*}
c_{\mathrm{CLD}}(i) = (1 + c_i) \sum_{j \in \mathcal{N}(i)} d_j,
\end{equation*}
where \( c_i \) denotes the clustering coefficient of node \( i \),
\( \mathcal{N}(i) \) is the set of neighbors of node \( i \),
and \( d_j \) represents the degree of neighbor \( j \). Hence, the CLD centrality accounts for both the number of neighbors and the connectivity among them.