Degree and structural hole count (DSHC) method
The
degree and structural hole count
(DSHC) method is a local centrality measure that combines information about a node's degree with the structural holes in its neighborhood [2]. The DSHC of node \(i\) is defined as
\[
c_{\mathrm{DSHC}}(i) = \sum_{j \in \mathcal{N}(i)} \left( \left( \frac{1}{d_i} + \frac{1}{d_j} \right) \frac{1}{1 + \Delta_{ij}} \right)^2,
\]
where \(\mathcal{N}(i)\) is the set of neighbors of node \(i\), \(d_i\) and \(d_j\) denote the degrees of nodes \(i\) and \(j\), respectively, and
\[
\Delta_{ij} = |\mathcal{N}(j) \setminus \mathcal{N}(i)|
\]
represents the number of structural holes between nodes \(i\) and \(j\), with node \(i\) acting as the intermediary. This measure captures both the local connectivity and the bridging role of a node within its neighborhood.