Fairness on the Web: Alternatives to the Power Law (WebSci 2012)

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Jérôme KUNEGIS

Automotive Technology Business

Fairness

Jérôme Kunegis & Julia Preusse Fairness on the Web: Alternatives to the Power Law
WebSci 2012 2 / 20

Jérôme Kunegis & Julia Preusse Fairness on the Web: Alternatives to the Power Law
WebSci 2012 3 / 20

The Pareto Principle

“20% of people own 80% of land.”
(In 1910s Italy)

(Pareto, 1919)

Jérôme Kunegis & Julia Preusse Fairness on the Web: Alternatives to the Power Law
WebSci 2012 4 / 20

A IR
N F
U

Jérôme Kunegis & Julia Preusse Fairness on the Web: Alternatives to the Power Law
WebSci 2012 5 / 20

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.
19.7% of all cats receive 80.3% of all friendships on Catster.com.
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 make up 76.9% of project memberships on Github.
27.3% of users receive 72.7% of replies on Digg.
27.6% of all hamsters receive 72.4% of all friendships on Hamsterster.com.
35.7% of all Twitter users receive 64.3% of all follows.
Jérôme Kunegis & Julia Preusse Fairness on the Web: Alternatives to the Power Law
WebSci 2012 6 / 20

Degree distribution
C(n) » n¡°

Jérôme Kunegis & Julia Preusse Fairness on the Web: Alternatives to the Power Law
WebSci 2012 7 / 20

TODO

Jérôme Kunegis & Julia Preusse Fairness on the Web: Alternatives to the Power Law
WebSci 2012 8 / 20

Which distribution is fairer?

Flickr friendships OR Digg replies

Jérôme Kunegis & Julia Preusse Fairness on the Web: Alternatives to the Power Law
WebSci 2012 9 / 20

Lorenz Curve – Gini Coefficient

Jérôme Kunegis & Julia Preusse Fairness on the Web: Alternatives to the Power Law
WebSci 2012 10 / 20

Flickr Digg

Jérôme Kunegis & Julia Preusse Fairness on the Web: Alternatives to the Power Law
WebSci 2012 11 / 20

Perfect Power Laws

Jérôme Kunegis & Julia Preusse Fairness on the Web: Alternatives to the Power Law
WebSci 2012 12 / 20

Entropy

High entropy

Low entropy

Jérôme Kunegis & Julia Preusse Fairness on the Web: Alternatives to the Power Law
WebSci 2012 13 / 20

@kunegis @beyonce @ststaab

@noshir @barabasi

Jérôme Kunegis & Julia Preusse Fairness on the Web: Alternatives to the Power Law
WebSci 2012 14 / 20

Entropy

Jérôme Kunegis & Julia Preusse Fairness on the Web: Alternatives to the Power Law
WebSci 2012 15 / 20

max He = ln jVj
Jérôme Kunegis & Julia Preusse Fairness on the Web: Alternatives to the Power Law
WebSci 2012 16 / 20

Normalized Entropy

Jérôme Kunegis & Julia Preusse Fairness on the Web: Alternatives to the Power Law
WebSci 2012 17 / 20

Gini vs Entropy

½ = ¡0.71
p < 0.001

Jérôme Kunegis & Julia Preusse Fairness on the Web: Alternatives to the Power Law
WebSci 2012 18 / 20

Comparison
Power Law Gini Norm. Entropy
Generality Power-law All networks All networks
Interpretation Many (!) Economy Physical
Runtime Slow Fast Fast
Coverage d(u) ≥ dmin All All

Jérôme Kunegis & Julia Preusse Fairness on the Web: Alternatives to the Power Law
WebSci 2012 19 / 20

Thank You
Jérôme Kunegis @kunegis
Julia Preusse

WeST – Institute for Web Science and Technologies
University of Koblenz–Landau, Germany

konect.uni-koblenz.de

Jérôme Kunegis & Julia Preusse Fairness on the Web: Alternatives to the Power Law
WebSci 2012 20 / 20

References
Pareto, V. Manuale di economia politica con una introduzione alla
scienza sociale (Manual of political economy). Milano : Societa
Editrice Libraria, 1919.

Jérôme Kunegis & Julia Preusse Fairness on the Web: Alternatives to the Power Law
WebSci 2012 21 / 20

Edge distribution Degree distribution
Jérôme Kunegis & Julia Preusse Fairness on the Web: Alternatives to the Power Law
WebSci 2012 22 / 20

…

Jérôme Kunegis & Julia Preusse Fairness on the Web: Alternatives to the Power Law
WebSci 2012 23 / 20

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In this talk, Jérôme Kunegis will present recent results on the measurement of conflict in signed social network. A signed social network is a network in which both positive and negative ties are present, for instance representing friendship and enmity, or trust and distrust. Such networks have long been studied under the aspect of balance theory, i.e., considering whether the individuals can be grouped into two groups, such that the sign of all ties reflects the partition, or equivalently in terms of the individual configuration of tryads. The failure of such a structure to be present in a signed social network is usually designated as conflict, and measuring the amount of conflict in a given signed social network is an open problem. In this talk, a novel measure of conflict is presented, based on algebraic graph theory, and considering a previously known variant of the Laplacian matrix for signed graphs. The talk will show both theoretical motivations for the measure, as well as an evaluation of its utility at signed social network analysis using multiple real-world signed social networks, based on networks from the KONECT project. Jérôme Kunegis from the Center for Complex Networks (naXys) at the University of Namur (Belgium) is the founder and main lead of the KONECT project, a curated collection of network datasets, algorithms and analyses, maintained at the University of Namur.

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