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