Neighborhood structure-based centrality (NSC)
The
neighborhood structure-based centrality
(NSC) is a hybrid measure that integrates the Lobby index (\(l\)-index) and the \(k\)-shell centrality of a node and its neighbors [2]. For a node \(i \in \mathcal{N}\), the NSC score \(c_{NSC}(i)\) is defined as
\[
c_{NSC}(i) = \frac{c_{Lobby}(i)}{\langle c_{Lobby} \rangle} + \frac{k_s(i)}{\langle k_s \rangle}
+ \sum_{j \in \mathcal{N}(i)} \left( \frac{c_{Lobby}(j)}{\langle c_{Lobby} \rangle} + \frac{k_s(j)}{\langle k_s \rangle} \right),
\]
where \(\mathcal{N}(i)\) denotes the set of neighbors of node \(i\), \(c_{Lobby}(i)\) is the Lobby index [3] of node \(i\), \(k_s(i)\) is its \(k\)-shell centrality, and \(\langle c_{Lobby} \rangle\) and \(\langle k_s \rangle\) are the mean values of the Lobby index and \(k\)-shell centrality, respectively.
Nodes with high NSC values are characterized by both strong individual influence (high Lobby index and/or \(k\)-shell index) and connections to other influential nodes, rendering them especially important for spreading processes and the structural integrity of the network.