Cc-Burt centrality
Cc-Burt
centrality is a hybrid centrality measure that combines the concept of
structural holes
with closeness centrality to identify key nodes in a network [2]. The structural hole theory accounts for both a node's degree and the topological relationships among its neighbors, while closeness centrality reflects the node's global position in the network.
For a node \(i\), the \textsc{Cc-Burt} centrality \(c_{\textsc{Cc-Burt}}(i)\) is defined as
\[
c_{\textsc{Cc-Burt}}(i) = \frac{1}{N} \left( \frac{1}{c_{cl}(i)} + \sum_{j \in \mathcal{N}(i)} \frac{c_{\mathrm{Burt}}(j)}{c_{cl}(j)} \right),
\]
where \(c_{cl}(i)\) is the closeness centrality of node \(i\) and \(c_{\mathrm{Burt}}(i)\) is the Burt's constraint of node \(i\).
The Cc-Burt centrality integrates local structural constraints and global network position to provide a more comprehensive evaluation of node influence.