Bridging centrality is a betweenness-based measure proposed in [2] to identify bridging nodes, which are the nodes that connect densely connected components in a network. The bridging centrality of node \(i\), denoted \(c_{\mathrm{bridging}}(i)\), is defined as the product of its betweenness centrality \(c_{\mathrm{betw}}(i)\) and its bridging coefficient \(β_c(i)\), capturing both global and local features of the node:
\begin{equation*}
c_{\mathrm{bridging}}(i) = c_{\mathrm{betw}}(i) \cdot β_c(i)
= \sum_{j=1}^{N} \sum_{k=1}^{N} \frac{σ_{jk}(i)}{σ_{jk}} \cdot \frac{d_i^{-1}}{\sum_{j \in \mathcal{N}(i)} d_j^{-1}},
\end{equation*}
where \(d_i\) is the degree of node \(i\), \(σ_{jk}\) is the number of shortest paths between nodes \(j\) and \(k\), and \(σ_{jk}(i)\) is the number of those paths that pass through node \(i\).
A higher \(c_{\mathrm{bridging}}(i)\) indicates that more information flows through node \(i\) (high betweenness) and that the node serves as a critical connector between densely connected regions (high bridging coefficient).

References

[1] Shvydun, S. (2025). Zoo of Centralities: Encyclopedia of Node Metrics in Complex Networks. arXiv: 2511.05122 https://doi.org/10.48550/arXiv.2511.05122
[2] Hwang, W., Cho, Y. R., Zhang, A., & Ramanathan, M. (2006). Bridging centrality: identifying bridging nodes in scale-free networks. In Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining (pp. 20-23).