# Étudier les formes de sociabilité

## Les mathématiques de Facebook

Maths Club

Univ. Paris-Diderot

8 février 2016

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Maths Club

Univ. Paris-Diderot

8 février 2016

- Distribution of number of contacts
- Short distances
- Triangles

3½ degrees of separation

- blog post by Facebook's Core Data Science team (2016)
- Backstrom et al., 2012
- Followup on Milgram, 1967, The small world problem

- Distances (average, diameter)
- Triangles

- Random graphs
*do have*very small distances - A path of length 5 is looooong
- (btw, Facebook's diameter is ~40)

Backstrom & Kleinberg, 2014

- predicts if ego is

"in a relationship" - if yes, guesses the lover with 50%
(only 25% when using shared friends)

- when bad dispersion value, twice as much likely to break within 2 months

- Given
*ego*and*alter*, - take ego's network without
*ego*and*alter*, **dispersion (u,v)**

= sum of distances between all pairs of nodes**distance (u,v)**

= 1 if*u*and*v*(friends of) friends of each other,

0 otherwise

- in collaboration with CSA poll agency
- a sample of 880 representative internet users
- 15 000 respondents
- large-scale personal network analysis
- ethnographic interviews