INF centrality
The
INF centrality
is a semi-local measure for identifying influential nodes in social networks [2]. Let \(\mathcal{N}^{(\leq l)}(i)\) denote the set of nodes within \(l\)-hop neighborhood of node \(i\). The centrality \(c_{\textsc{INF}}(i)\) of node \(i\) is defined as
\begin{equation*}
c_{\textsc{INF}}(i) =
\sum_{j \in \mathcal{N}^{(\leq l)}(i)} \frac{d_{ij}^2\, w_{ij}}{d_j},
\end{equation*}
where \(d_{ij}\) is the shortest-path distance between nodes \(i\) and \(j\), \(w_{ij}\) is the weight of edge \((i,j)\), and \(d_j\) is the degree of node \(j\). Huang et al. [2] set \(l=1\) as the truncated radius.
For unweighted networks, the INF centrality simplifies to
\begin{equation*}
c_{\textsc{INF}}(i) = \sum_{j \in \mathcal{N}(i)} \frac{1}{d_j},
\end{equation*}
emphasizing the influence of nodes connected to low-degree neighbors.