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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.

Jon Kleinberg studies algorithms and networks, including how the link structure of information can reveal useful organization. His work on the HITS algorithm assigns separate authority and hub scores to web pages: an authority is supported by good hubs, while a hub points to good authorities.^[ref]

If $A_{ij}=1$ when page $i$ links to page $j$, the updates take the form $a\leftarrow A^{T}h$ and $h\leftarrow Aa$, with normalization. Combining them gives a power iteration on $A^{T}A$ for authority scores and on $A{A}^T$ for hub scores. Thus the apparently circular verbal definition becomes a numerical eigenvector problem rather than an infinite regress. Link structure supplies a ranking signal, not a guarantee of truth.

With Éva Tardos, Kleinberg also wrote the algorithms textbook Algorithm Design; his institutional page identifies network structure as a central research theme.^[ref]

By Elliot Anshelevich, Anirban Dasgupta, Jon Kleinberg, Éva Tardos, Tom Wexler, Tim Roughgarden.

Author-hosted manuscript dated 17 June 2004. Introduction defines the cost ratio for the best Nash equilibrium and explains the stable-recommendation interpretation.