Lhc index
Lhc index
is a hybrid approach for identifying highly influential spreaders in complex networks. It integrates both neighbor information and topological connectivity information among neighboring nodes [2]. The neighbor information is represented by the degree of a node, which reflects the number of its direct connections. The connectivity among a node’s neighbors is characterized by the number of triangular structures centered on that node, indicating how tightly its neighbors are interconnected.
The centrality \( c_{\textsc{lhc}}(i) \) of node \( i \) is defined as
\begin{equation*}
c_{\textsc{lhc}}(i) =
\sum_{j \in \mathcal{N}(i)}
\sum_{l \in \mathcal{N}^{(\leq k)}(j)}
\frac{
d_l \left( 1 + \frac{\Delta_l}{\Delta} \right)
}{d_{jl}^2},
\end{equation*}
where \( \mathcal{N}^{(\leq k)}(j) \) denotes the set of nodes within the \(k\)-hop neighbourhood of node \(j\), \( d_{jl} \) is the shortest-path distance between nodes \( j \) and \( l \), \( d_l \) is the degree of node \( l \), \( \Delta_l \) is the number of triangles including node \( l \), and \( \Delta \) is the total number of triangular structures in the network.
To reduce computational complexity, Wang et al. [2] set the distance parameter to \( k = 2 \).