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Small World Networks Antonio Fernndez Anta S enior Researcher - - PowerPoint PPT Presentation
Small World Networks Antonio Fernndez Anta S enior Researcher - - PowerPoint PPT Presentation
Small World Networks Antonio Fernndez Anta S enior Researcher Overview of the talk Graphs and networks. S mall world networks. Applications. Origin of the S tudy of Networks Knigsberg bridges (Kaliningrad), XVIIIth
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Overview of the talk
- Graphs and networks.
- S
mall world networks.
- Applications.
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Origin of the S tudy of Networks
Königsberg bridges (Kaliningrad), XVIIIth century. Is there a cycle crossing each bridge only once?
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Euler to the Rescue!
Leonhar Euler solved this brainteaser in 1736.
Trick: think out of the box.
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First step: model
Problem modeling
node vertex edge link
network graph
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S econd step: solve
There is no solution!!
No network with odd degree nodes can be traversed with a cycle.
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Networks Everywhere!!
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Maps Are Networks
How would you find the best route for a salesperson?
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S
- cial Networks
How many hops from me to Obama?
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S mall World
Milgram explored (1967) social distances in US
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S ix Degrees of S eparation
On average, the target person was reached in 6 hops.
It is a small world!!
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Bacon Number
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S
- cial Networks
They connect many people with a few hops
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Example: Linkedin
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My Network
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Distances
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Distances
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S mall World Networks
- Networks with small distances
- Beyond social networks:
– Internet and the web. – Neurons – Infection – The grid – Metabolic – … .
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Applications
S earch of resources (files)
(x,y)
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Conclusions
- Networks are everywhere
- Many of them have small world properties
- We would like to use these properties for our
benefit
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That’ s all :-)
Questions?
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