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Workshop: The Future of Web Search

Graph Fibrations, graph isomorphism and PageRank

author: Paolo Boldi, University of Milano
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Slides
0:00 Graph brations, graph isomorphism, and PageRank
1:08 Things related to PageRank
1:50 Covering projections in algebraic topology
2:35 Covering projections in modern mathematics
4:15 From covering projections to brations
5:52 My own personal relation with brations
7:58 A graph is a graph is a graph. . .
8:48 Graph morphisms
9:39 Graph bration
10:48 Graph bration
11:28 A graph bration is. . .
12:14 A graph bration is. . .
12:21 A basic ingredient: universal total graph
13:32 Basic property of universal total graphs
15:00 Minimum base
16:12 Markov chains and graphs
17:35 Markov chains with restart
19:18 PageRank as a special case
19:36 PageRank: an example
19:49 Markov chains with restart are unichain
20:39 Invariant distribution and limit behaviours
21:07 Power series associated to a graph
23:06 Power series associated to a graph
23:15 Power series and brations
23:25 An example
23:43 Consequences
24:02 Power series associated to a graph
24:20 Consequences
24:46 Markovian spectrally distinguishable graphs
26:21 Graph brations and graph isomorphism
27:51 Experimental results

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