Borgatti’s effective size , introduced by [2], is a simplified reformulation of Burt’s effective size measure [3]. It defines the effective size \( c_{\mathrm{BES}}(i) \) of ego \( i \)’s network as
\begin{equation*}
c_{\mathrm{BES}}(i) = d_i - c_{r}(i),
\end{equation*}
where \( d_i \) denotes the degree of node \( i \), and \( c_{r}(i) \) represents the redundancy measure also proposed by [2]. This formulation expresses the number of non-redundant contacts in ego \( i \)’s network, emphasizing that relationships linking \( i \) to otherwise unconnected individuals provide access to diverse and independent sources of information or resources.

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] Borgatti, S. P. (1997). Structural holes: Unpacking Burt’s redundancy measures. Connections, 20(1), 35-38.
[3] Burt, R.S. & Holes, S. (1992). Structural Holes: The Social Structure of Competition. Harvard University Press, Cambridge, MA.