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Étudier les formes de sociabilité

Les mathématiques de Facebook

Christophe Prieur,
Télécom ParisTech, dept. SES, I3

Maths Club

Univ. Paris-Diderot

8 février 2016

"social network" de 1950 à 2008
1938 : Jacob Levy Moreno
1954 : John Barnes
1950-60 : anthropologie et maths
théorie des graphes
1970 : Harrison White
1990 : Le web
1998 : Google
le pagerank
1998 : les "petits mondes"
"complex networks"

Facebook's
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

How to compute that?

  • Distances (average, diameter)
  • Triangles
A word on graph algorithms...

Small world, close horizon

  • Random graphs do have very small distances
  • A path of length 5 is looooong
  • (btw, Facebook's diameter is ~40)
2007 : Facebook's newsfeed
structure of personal networks

What makes good couples?

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

Dispersion

  • 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

Algopol: a mixed research framework

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

Facebook ties

talking religion or politics?

A Facebook app

app.algopol.fr

data-based interviews