All-around score
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
.