The extended local bridging centrality (ELBC), also known as the 2-hop local bridging centrality (LBC2) or Extended LBC, extends the localized bridging centrality by incorporating information from a broader, two-hop neighborhood around each node [2]. It is defined as\begin{equation*}c_{\mathrm{LBC2}}(i) = c_{\mathrm{ego2}}(i) \cdot β_c(i),\end{equation*}where \(c_{\mathrm{ego2}}(i)\) denotes the betweenness centrality of node \(i\) computed within its 2-hop egocentric network, and \(β_c(i)\) is the bridging coefficient of node \(i\). This extension captures not only the immediate (1-hop) brokerage of a node but also its mediating role across the next layer of neighbors, offering a more comprehensive view of local connectivity.

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] Macker, J. P. (2016). An improved local bridging centrality model for distributed network analytics. In MILCOM 2016-2016 IEEE Military Communications Conference (pp. 600-605). IEEE. doi: 10.1109/MILCOM.2016.7795393. doi: 10.1109/MILCOM.2016.7795393.