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PageRank

PageRank. Brin, Page description: C. Faloutsos, CMU. Problem definition:. Given a directed graph which are the most ‘important’ nodes?. 2. 1. 3. 4. 5. google/Page-rank algorithm. Imagine a particle randomly moving along the edges (*) compute its steady-state probabilities

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PageRank

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  1. PageRank Brin, Page description: C. Faloutsos, CMU

  2. Problem definition: • Given a directed graph • which are the most ‘important’ nodes? 2 1 3 4 5 C. Faloutsos

  3. google/Page-rank algorithm • Imagine a particle randomly moving along the edges (*) • compute its steady-state probabilities (*) with occasional random jumps C. Faloutsos

  4. google/Page-rank algorithm • that is: given a Markov Chain, compute the steady state probabilities p1 ... p5 2 1 3 4 5 C. Faloutsos

  5. 2 1 3 4 5 (Simplified) PageRank algorithm • Let W be the transition matrix (= adjacency matrix); let A be WT, and column-normalized - then From A To = C. Faloutsos

  6. (Simplified) PageRank algorithm • A p = p A p = p 2 1 3 = 4 5 C. Faloutsos

  7. (Simplified) PageRank algorithm • A p = 1 * p • thus, p is the eigenvector that corresponds to the highest eigenvalue(=1, since the matrix is column-normalized) C. Faloutsos

  8. (Simplified) PageRank algorithm • In short: imagine a particle randomly moving along the edges • compute its steady-state probabilities Full version of algo: with occasional random jumps C. Faloutsos

  9. Full Algorithm • With probability 1-c, fly-out to a random node • Then, we have p = c Ap + (1-c)/n 1 => p = (1-c)/n [I - c A] -1 1 C. Faloutsos

  10. Impact - current research • multi-billion $ company • over 2,500 citations (Google scholar) • Topic-Sensitive PageRank [Haveliwala+] • TrustRank [Gyongyi+] • Efficient computation • ObjectRank [Papakonstantinou+] • centerPiece subgraphs [Tong+] • ... C. Faloutsos

  11. Brin, S. and L. Page (1998). Anatomy of a Large-Scale Hypertextual Web Search Engine. 7th Intl World Wide Web Conf. References C. Faloutsos

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