Graph Fibrations, graph isomorphism and PageRank

Posted in Science on July 25, 2008


Graph Fibrations, graph isomorphism and PageRank

Lecture slides:

  • Things related to PageRank
  • Covering projections in algebraic topology
  • Covering projections in modern mathematics
  • From covering projections to fibrations
  • My own personal relation with fibrations
  • A graph is a graph is a graph...
  • Graph morphisms
  • Graph fibration
  • A graph fibration is...
  • A basic ingredient: universal total graph
  • Basic property of universal total graphs
  • Minimum base
  • Markov chains and graphs
  • Markov chains with restart
  • PageRank as a special case
  • PageRank: an example
  • Markov chains with restart are unichain
  • Invariant distribution and limit behaviours
  • Power series associated to a graph
  • Power series and fibrations
  • An example
  • Consequences
  • Power series associated to a graph
  • Consequences
  • Markovian spectrally distinguishable graphs
  • Graph fibrations and graph isomorphism
  • Experimental results

Author: Paolo Boldi, University of Milano

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