Semi-local degree and clustering coefficient (SLDCC)
The
semi-local degree and clustering coefficient
(SLDCC) is a hybrid centrality measure that evaluates the influence of a node based on its degree, clustering coefficient and the clustering coefficients of its second-level neighbors [2]. Berahmand et al. [2] argue that a node with high degree but low clustering coefficient can be considered a structural hole in the network, bridging otherwise disconnected regions. Furthermore, if the sum of the clustering coefficients of a node's second-level neighbors is high, it indicates that these neighbors reside in a densely connected part of the network.
The centrality of node \(i\) is defined as
\[
c_{SLDCC}(i) = \frac{d_i}{c_i + \frac{1}{d_i}} + \sum_{j \in \mathcal{N}^{(2)}(i)} c_j,
\]
where \(d_i\) and \(c_i\) are the degree and clustering coefficient of node \(i\), and \(\mathcal{N}^{(2)}(i)\) denotes the set of second-level neighbors of \(i\).
Thus, the SLDCC measure combines three aspects: the degree of the node, the negative effect of its own clustering coefficient, and the positive effect of the clustering coefficients of its second-level neighbors.