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The rank value indicates an importance of a particular page. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). A page that is linked to by many pages with high PageRank receives a high rank itself.
PageRank works by counting the number and quality of links to a page to determine a rough estimate of how important the website is. The underlying assumption is that more important websites are likely to receive more links from other websites. [1] However, Google claims there will be no more PageRank updates, rendering this metric as outdated. [2]
Fig.1. Google matrix of Wikipedia articles network, written in the bases of PageRank index; fragment of top 200 X 200 matrix elements is shown, total size N=3282257 (from [1]) A Google matrix is a particular stochastic matrix that is used by Google's PageRank algorithm. The matrix represents a graph with edges representing links between pages.
Ranking of query is one of the fundamental problems in information retrieval (IR), [1] the scientific/engineering discipline behind search engines. [2] Given a query q and a collection D of documents that match the query, the problem is to rank, that is, sort, the documents in D according to some criterion so that the "best" results appear early in the result list displayed to the user.
HITS, like Page and Brin's PageRank, is an iterative algorithm based on the linkage of the documents on the web. However it does have some major differences: It is processed on a small subset of ‘relevant’ documents (a 'focused subgraph' or base set), instead of the set of all documents as was the case with PageRank.
The pagerank is a highly unstable measure, showing frequent rank reversals after small adjustments of the jump parameter. [18] While the failure of centrality indices to generalize to the rest of the network may at first seem counter-intuitive, it follows directly from the above definitions. Complex networks have heterogeneous topology.
In information retrieval, Okapi BM25 (BM is an abbreviation of best matching) is a ranking function used by search engines to estimate the relevance of documents to a given search query.
Discounted cumulative gain (DCG) is a measure of ranking quality in information retrieval.It is often normalized so that it is comparable across queries, giving Normalized DCG (nDCG or NDCG).