Degree and Importance of Lines (DIL)
The
Degree and Importance of Lines (DIL) centrality
evaluates the importance of a node based on its degree and the significance of its adjacent links [2]. The DIL measure reflects that the influence of a node depends on both its degree and the structural roles of its adjacent links. The centrality \( c_{\mathrm{DIL}}(i) \) of node \( i \) is defined as
\begin{equation*}
c_{\mathrm{DIL}}(i) = d_i + \sum_{j \in \mathcal{N}(i)}
\left( \frac{(d_i - \Delta_{ij} - 1)(d_j - \Delta_{ij} - 1)}{\Delta_{ij}/2 + 1} \right)
\left( \frac{d_i - 1}{d_i + d_j - 2} \right),
\end{equation*}
where \( d_i \) is the degree of node \( i \),
\( \mathcal{N}(i) \) is the set of neighbors of \( i \), and
\( \Delta_{ij} \) is the number of triangles that include the link \((i,j)\).