= HITS algorithm
{c}
{title2=$a\leftarrow A^{\mathsf T}h,\ h\leftarrow Aa$}
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.<Authoritative Sources in a Hyperlinked Environment by Jon Kleinberg>[§2, hubs, authorities and iterative weight updates]{ref}
Let the <adjacency matrix> satisfy $A_{ij}=1$ when page $i$ links to page $j$. With authority <vector> $a$ and hub <vector> $h$, alternate
$$
a\leftarrow A^{\mathsf T}h,\qquad h\leftarrow Aa,
$$
normalizing 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.
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