The all-around score , also known as the degree-betweenness-\(k\)-shell (DBK) index, aims to identify nodes that perform well across multiple centrality dimensions simultaneously [2]. The all-around centrality of a node \(i\) is defined as the Euclidean distance in the normalized centrality space spanned by degree, betweenness, and \(k\)-shell measures:
\begin{equation*}
c_{\mathrm{AA}}(i) = \sqrt{\overline{c}_d^2(i) + \overline{c}_b^2(i) + \overline{c}_k^2(i)},
\end{equation*}
where \(\overline{c}_d(i)\), \(\overline{c}_b(i)\), and \(\overline{c}_k(i)\) denote the normalized degree, betweenness, and \(k\)-shell centrality scores of node \(i\), respectively.
Nodes with high all-around scores achieve strong performance across all three dimensions and are thus referred to as all-around nodes .

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] Hou, B., Yao, Y., & Liao, D. (2012). Identifying all-around nodes for spreading dynamics in complex networks. Physica A: Statistical Mechanics and its Applications, 391(15), 4012-4017. doi: 10.1016/j.physa.2012.02.033.