HITS algorithm ($a\leftarrow A^{\mathsf{T}}h,h\leftarrow Aa$)

The HITS algorithm assigns two related scores to pages in a selected link graph: an authority score for being linked to by strong hubs, and a hub score for linking to strong authorities. Jon Kleinberg formulated this mutual reinforcement to identify useful sources for broad-topic web queries.^[ref]

Let the adjacency matrix satisfy $A_{ij}=1$ when page $i$ links to page $j$. With authority vector $a$ and hub vector $h$, alternatenormalizing after each update. Repeated authority updates involve $A^{\mathsf{T}}A$, connecting the procedure to power iteration and eigenvectors. If pages one and two each link only to page three, the third page becomes the authority and the first two equally strong hubs. A high score describes this link structure; it is not independent verification of the page's claims.