fairness on the web: alternatives to the power law
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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
Fairness on the Web: Alternatives to the Power Law4 / 19
Edge distribution Degree distribution
Jérôme Kunegiskunegis@uni-koblenz.de
Fairness on the Web: Alternatives to the Power Law5 / 19
Power-law degree distribution
C(n) ~ n−γ
Jérôme Kunegiskunegis@uni-koblenz.de
Fairness on the Web: Alternatives to the Power Law6 / 19
TODO
Jérôme Kunegiskunegis@uni-koblenz.de
Fairness on the Web: Alternatives to the Power Law7 / 19
todo
Flickr Digg
Jérôme Kunegiskunegis@uni-koblenz.de
Fairness on the Web: Alternatives to the Power Law8 / 19
The Pareto Principle
20% of people own 80% of land.
(In 1920 Italy)
Jérôme Kunegiskunegis@uni-koblenz.de
Fairness on the Web: Alternatives to the Power Law9 / 19
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
Fairness on the Web: Alternatives to the Power Law10 / 19
Gini Coefficient – Lorenz Curve
Jérôme Kunegiskunegis@uni-koblenz.de
Fairness on the Web: Alternatives to the Power Law11 / 19
todo
Jérôme Kunegiskunegis@uni-koblenz.de
Fairness on the Web: Alternatives to the Power Law12 / 19
Zeta distribution C(n) = n−γ / ζ(γ)
Jérôme Kunegiskunegis@uni-koblenz.de
Fairness on the Web: Alternatives to the Power Law13 / 19
Random Edge→Vertex
P(u) = d(u) / 2|E|
Jérôme Kunegiskunegis@uni-koblenz.de
Fairness on the Web: Alternatives to the Power Law14 / 19
Entropy
Jérôme Kunegiskunegis@uni-koblenz.de
Fairness on the Web: Alternatives to the Power Law15 / 19
Maximum Entropy
max He = ln |V|
Jérôme Kunegiskunegis@uni-koblenz.de
Fairness on the Web: Alternatives to the Power Law16 / 19
Normalized Entropy
Jérôme Kunegiskunegis@uni-koblenz.de
Fairness on the Web: Alternatives to the Power Law17 / 19
Jérôme Kunegiskunegis@uni-koblenz.de
Fairness on the Web: Alternatives to the Power Law18 / 19
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
Fairness on the Web: Alternatives to the Power Law19 / 19
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)
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