# Graph fibrations, graph isomorphism, and PageRank

Paolo Boldi; Violetta Lonati; Massimo Santini; Sebastiano Vigna

RAIRO - Theoretical Informatics and Applications (2006)

- Volume: 40, Issue: 2, page 227-253
- ISSN: 0988-3754

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topBoldi, Paolo, et al. "Graph fibrations, graph isomorphism, and PageRank." RAIRO - Theoretical Informatics and Applications 40.2 (2006): 227-253. <http://eudml.org/doc/249717>.

@article{Boldi2006,

abstract = {
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
O(n) space occupancy (where n is the number of nodes) may be acceptable, but
O(m) is not (where m is the number of arcs).
},

author = {Boldi, Paolo, Lonati, Violetta, Santini, Massimo, Vigna, Sebastiano},

journal = {RAIRO - Theoretical Informatics and Applications},

keywords = {Graph fibrations; PageRank; Markov chain with restart.; graph fibrations; Markov chain with restart},

language = {eng},

month = {7},

number = {2},

pages = {227-253},

publisher = {EDP Sciences},

title = {Graph fibrations, graph isomorphism, and PageRank},

url = {http://eudml.org/doc/249717},

volume = {40},

year = {2006},

}

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

DA - 2006/7//

PB - EDP Sciences

VL - 40

IS - 2

SP - 227

EP - 253

AB -
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
O(n) space occupancy (where n is the number of nodes) may be acceptable, but
O(m) is not (where m is the number of arcs).

LA - eng

KW - Graph fibrations; PageRank; Markov chain with restart.; graph fibrations; Markov chain with restart

UR - http://eudml.org/doc/249717

ER -

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