Convergence of HITS

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Convergence of HITS (hyperlink-induced topic
search) algorithm by Victor Boyarshinov
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• Was first introduced by Jon M. Kleinberg (1998).
  
• Assumption a topic can be roughly divided into
  pages with good coverage of the topic, called
  authorities, and directory-like pages with many
  hyperlinks to useful pages on the topic, called
  hubs.
• And the goal of HITS is basically to identify
  good authorities and hubs for a certain topic
  which is usually defined by the user's query.
• Given a user query, the HITS algorithm first
  creates a neighborhood graph for the query.
  Then, an iterative calculation was performed on
  the value of authority and value of hub.

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For each page p , the authority and hub values
are computed as follows The authority value of
page p is the sum of hub scores of all the pages
that points to p The hub value of page p is the
sum of authority scores of all the pages that p
points to
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• Algorithm Complexity
• Time complexity of one iteration of the HITS
  algorithm is O(E(G)).
• Experimental Data
• The algorithm was tested on uniformly generated
  directed random graphs.
• The edge probability value was tuned so that
  expected value for out-degree of every vertex was
  10.
• Convergence Criterion
• Iterations were performed until sum of absolute
  values of weight changes fall below constant
  threshold (0.0000001).

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Goal of the Experiments Determine how number of
iterations increases with size of graph if
average degree of a vertex remains the same
(10). Experiments results
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The reason why attempt of convergence rate
estimating failed is insufficient number of tests
(computationally expensive!) Another set of test
examples was generated as follows take two
disjoint uniformly generated random graphs of
size n, take any vertex v from the first graph,
vertex u from the second graph and connect the
components by adding edges (u, v) and (v, u).
Experiments results