KDEC method
The
KDEC
method identifies influential nodes by combining the gravity model with the concept of effective distance [2]. In this model, a node's mass is given by the product of its degree and \(k\)-shell index, while the shortest-path distance is replaced by the effective distance to better capture the network's dynamic spreading pathways.
Let \(\mathcal{N}^{(\leq l)}(i)\) denote set of nodes within the \(l\)-hop neighbourhood of node \(i\). The centrality \( c_{\textsc{KDEC}}(i) \) of node \( i \) is defined as
\begin{equation*}
c_{\textsc{KDEC}}(i) =
\sum_{j \in \mathcal{N}^{(\leq l)}(i)}
\frac{m(i)\, m(j)}{\tilde{d}_{ij}^2},
\end{equation*}
where \( \tilde{d}_{ij} \) is the
effective shortest-path distance
proposed by Brockmann and Helbing [3]. The parameter \( m(i) \) represents the mass of node \( i \), given by
\begin{equation*}
m(i) = d_i \cdot k_s(i),
\end{equation*}
where \( d_i \) is the degree of node \( i \) and \( k_s(i) \) is its \(k\)-shell index. Zhang et al. [2] consider \( l = 2 \) as the truncated radius.