PageRank is a ranking method that assigns scores to web pages using the limit distribution of a random walk on the web graph. A fibration of graphs is a morphism that is a local isomorphism of in-neighbourhoods, much in the same way a covering projection is a local isomorphism of neighbourhoods. We show that a deep connection relates fibrations and Markov chains with restart, a particular kind of Markov chains that include the PageRank one as a special case. This fact provides constraints on the values that PageRank can assume. Using our results, we show that a recently defined class of graphs that admit a polynomial-time isomorphism algorithm based on the computation of PageRank is really a subclass of fibration-prime graphs, which possess simple, entirely discrete polynomial-time isomorphism algorithms based on classical techniques for graph isomorphism. We discuss efficiency issues in the implementation of such algorithms for the particular case of web graphs, in which space occupancy (where is the number of nodes) may be acceptable, but is not (where is the number of arcs).
Mots clés : graph fibrations, pagerank, Markov chain with restart
@article{ITA_2006__40_2_227_0,
author = {Boldi, Paolo and Lonati, Violetta and Santini, Massimo and Vigna, Sebastiano},
title = {Graph fibrations, graph isomorphism, and pagerank},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
pages = {227--253},
publisher = {EDP-Sciences},
volume = {40},
number = {2},
year = {2006},
doi = {10.1051/ita:2006004},
mrnumber = {2252637},
zbl = {1112.68002},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/ita:2006004/}
}
TY - JOUR AU - Boldi, Paolo AU - Lonati, Violetta AU - Santini, Massimo AU - Vigna, Sebastiano TI - Graph fibrations, graph isomorphism, and pagerank JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2006 SP - 227 EP - 253 VL - 40 IS - 2 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ita:2006004/ DO - 10.1051/ita:2006004 LA - en ID - ITA_2006__40_2_227_0 ER -
%0 Journal Article %A Boldi, Paolo %A Lonati, Violetta %A Santini, Massimo %A Vigna, Sebastiano %T Graph fibrations, graph isomorphism, and pagerank %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2006 %P 227-253 %V 40 %N 2 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ita:2006004/ %R 10.1051/ita:2006004 %G en %F ITA_2006__40_2_227_0
Boldi, Paolo; Lonati, Violetta; Santini, Massimo; Vigna, Sebastiano. Graph fibrations, graph isomorphism, and pagerank. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 40 (2006) no. 2, pp. 227-253. doi : 10.1051/ita:2006004. http://archive.numdam.org/articles/10.1051/ita:2006004/
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