Neighborhood core diversity centrality (Cncd)
The
neighborhood core diversity centrality
(Cncd) is inspired by the extended neighborhood coreness (ENC) [2] and incorporates information entropy to quantify path diversity [3].
First, the path diversity \(p(i)\) of node \(i\) is defined as the ratio of its degree \(d_i\) to the sum of the degrees of its neighbors:
\[
p(i) = \frac{d_i}{\sum_{j \in \mathcal{N}(i)} d_j}.
\]
The \textsc{Cncd} centrality \(c_{\textsc{Cncd}}(i)\) of node \(i\) is then defined as
\[
c_{\textsc{Cncd}}(i) = c_{nc+}(i) + δ \, \frac{\sum_{j \in \mathcal{N}(i)} p(j) \ln p(j)}{\ln(1/d_i)} \, \frac{\sum_{j \in \mathcal{N}(i)} c_{nc+}(j)}{c_{nc+}(i)},
\]
where \(c_{nc+}(i)\) is the extended neighborhood coreness of node \(i\) as defined in [2] and \(δ\) is a tunable parameter (e.g., \(δ = 2\)).
The Cncd measure captures both the coreness of a node and the diversity of paths in its local neighborhood, providing a more nuanced evaluation of influence in complex networks.