HITS (Hubs and Authorities)
The
Hyperlink-Induced Topic Search (HITS)
algorithm was originally introduced in [2]. It assigns two scores to each node: the
hub score
and the
authority score
. A node \(i\) has a high hub score \(c_{\text{hub}}(i)\) if it links to nodes with high authority scores, i.e.,
\begin{equation*}
c_{\text{hub}}(i) = \sum_{j=1}^{N} a_{ij} \, c_{\text{authority}}(j),
\end{equation*}
where \(a_{ij}\) denotes the adjacency matrix element from node \(i\) to node \(j\). Similarly, a node \(i\) has a high authority score \(c_{\text{authority}}(i)\) if it is pointed to by nodes with high hub scores:
\begin{equation*}
c_{\text{authority}}(i) = \sum_{j=1}^{N} a_{ji} \, c_{\text{hub}}(j).
\end{equation*}
The iterative calculation of HITS can be formulated as an eigenvalue problem. Specifically, the hub and authority vectors correspond to the principal eigenvectors of \(AA^T\) and \(A^TA\), respectively, associated with the largest eigenvalue \(λ_{\max}\) of \(AA^T\) (or equivalently \(A^TA\)). In practice, HITS is designed for directed networks. For undirected networks, the hub and authority scores are identical and reduce to the standard eigenvector centrality.