Web Science and Technologies

University of Koblenz–Landau, Germany

Fairness on the Web:Alternatives to the Power Law

Jérôme KunegisUniversity of Koblenz–Landau

(with Julia Preusse)GESIS Cologne, Mai 2012

Jérôme Kunegiskunegis@uni-koblenz.de

Fairness on the Web: Alternatives to the Power Law2 / 19

Jérôme Kunegiskunegis@uni-koblenz.de

Fairness on the Web: Alternatives to the Power Law3 / 19

UNFAIR

Jérôme Kunegiskunegis@uni-koblenz.de

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Edge distribution Degree distribution

Jérôme Kunegiskunegis@uni-koblenz.de

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Power-law degree distribution

C(n) ~ n−γ

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TODO

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todo

Flickr Digg

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The Pareto Principle

20% of people own 80% of land.

(In 1920 Italy)

Jérôme Kunegiskunegis@uni-koblenz.de

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8.9% of bands make up 91.1% of plays on Last.fm.

14.6% of user groups account for 75.4% of group memberships on Flickr.

17.4% of movies receive 82.6% of ratings on MovieLens.

17.7% of profiles receive 82.3% of ratings on Czech dating site Libimseti.cz.

20.3% of all users receive 79.7% of “friend” and “foe” links on Slashdot.

21.3% of users receive 78.7% of wall posts on Facebook.

22.9% of users make up 77.1% of all “@” mentions on Twitter.

23.1% of projects receive 76.9% of project memberships on Github.

27.3% of users receive 72.7% of replies on Digg.

30.4% of all sites receive 69.6% of all hyperlinks on the Web.

Jérôme Kunegiskunegis@uni-koblenz.de

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Gini Coefficient – Lorenz Curve

Jérôme Kunegiskunegis@uni-koblenz.de

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todo

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Zeta distribution C(n) = n−γ / ζ(γ)

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Random Edge→Vertex

P(u) = d(u) / 2|E|

Jérôme Kunegiskunegis@uni-koblenz.de

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Entropy

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Maximum Entropy

max He = ln |V|

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Normalized Entropy

Jérôme Kunegiskunegis@uni-koblenz.de

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Jérôme Kunegiskunegis@uni-koblenz.de

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Generality

Interpretation

Runtime

Coverage

Power Law

Power-law

–––

Slow

d(u) ≥ dmin

Gini

All networks

Economy

Fast

All

Norm. Entropy

All networks

Physical

Fast

All

Comparison

Jérôme Kunegiskunegis@uni-koblenz.de

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http://konect.uni-koblenz.de/plots/degree_distribution

http://konect.uni-koblenz.de/plots/lorenz_curve

Thank You!→ 22 - 24 June, Web Science Conference

Dr. Jérôme Kunegis<kunegis@uni-koblenz.de>Institute for Web Science and TechnologiesUniversity of Koblenz–Landau (Campus Koblenz)