# 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*