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Web Science and Technologies                          University of Koblenz–Landau, GermanyWhy Beyoncé Is More Popular Tha...
FairnessJérôme Kunegis                        Why Beyoncé Is More Popular Than MeAlbert-Ludwigs-Universität Freiburg      ...
Jérôme Kunegis                        Why Beyoncé Is More Popular Than MeAlbert-Ludwigs-Universität Freiburg              ...
(1) The Pareto Principle“20% of people own 80% of land.”                 (In 1910s Italy)                                 ...
A IR                             N F                            UJérôme Kunegis                        Why Beyoncé Is More...
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.   ...
Degree distribution                                       C(n) » n¡° Jérôme Kunegis                            Why Beyoncé...
TODO       Jérôme Kunegis                        Why Beyoncé Is More Popular Than Me       Albert-Ludwigs-Universität Frei...
Which distribution is fairer?Flickr    friendships OR                   Digg    replies     Jérôme Kunegis                ...
Lorenz Curve – Gini Coefficient    Jérôme Kunegis                        Why Beyoncé Is More Popular Than Me    Albert-Lud...
Flickr                                 Digg Jérôme Kunegis                        Why Beyoncé Is More Popular Than Me Albe...
Perfect Power LawsJérôme Kunegis                        Why Beyoncé Is More Popular Than MeAlbert-Ludwigs-Universität Frei...
(2) Entropy                                            High entropy                                            Low entropy...
@kunegis                  @beyonce              @ststaab            @noshir                      @barabasi   Jérôme Kunegi...
EntropyJérôme Kunegis                        Why Beyoncé Is More Popular Than MeAlbert-Ludwigs-Universität Freiburg       ...
max He = ln jVjJérôme Kunegis                        Why Beyoncé Is More Popular Than MeAlbert-Ludwigs-Universität Freibur...
Normalized EntropyJérôme Kunegis                        Why Beyoncé Is More Popular Than MeAlbert-Ludwigs-Universität Frei...
Gini vs Entropy          ½ = ¡0.71          p < 0.001Jérôme Kunegis                        Why Beyoncé Is More Popular Tha...
(3) Random Walks Diversity                                   No diversityPret(L) large                              Pret(L...
Weighted Spectral DistributionPret(L) = §(i, j, . . . k) (d(i) d(j) . . . d(k)){1                  = tr(NL)               ...
Eigenvalues of NJérôme Kunegis                        Why Beyoncé Is More Popular Than MeAlbert-Ludwigs-Universität Freibu...
(4) ControllabilityDiversity                                        No diversity                                        (L...
Find a maximal directed 2-matching   #Knobs needed = jVj { max jMj     Jérôme Kunegis                        Why Beyoncé I...
Comparison               Power Law         Gini             Norm. Entropy Random walks ControllabilityGenerality     Power...
Network EvolutionJérôme Kunegis                        Why Beyoncé Is More Popular Than MeAlbert-Ludwigs-Universität Freib...
“The Rich Get Richer”(Barabási & Albert 1999)                  Jérôme Kunegis                        Why Beyoncé Is More P...
“R                 an                   do                               m                                      Wa        ...
“Ne                              two                                 rks                                       Get        ...
Experiments       20 networks from konect.uni-koblenz.de       9 authorship, 3 communication, 3 social, 3       interactio...
Thank YouJérôme Kunegis                                            @kunegisWork in collaboration with Julia Preusse, Serge...
ReferencesJ. Kunegis, S. Sizov, F. Schwagereit, D. Fay. Diversity Dynamics in OnlineNetworks. Proc. Conf. on Hypertext and...
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Why Beyoncé Is More Popular Than Me – Fairness, Diversity and Other Measures

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  1. 1. Web Science and Technologies University of Koblenz–Landau, GermanyWhy Beyoncé Is More Popular Than Me Fairness, Diversity and Other Measures Jérôme Kunegis Albert-Ludwigs-Universität Freiburg July 27, 2012
  2. 2. FairnessJérôme Kunegis Why Beyoncé Is More Popular Than MeAlbert-Ludwigs-Universität Freiburg 2
  3. 3. Jérôme Kunegis Why Beyoncé Is More Popular Than MeAlbert-Ludwigs-Universität Freiburg 3
  4. 4. (1) The Pareto Principle“20% of people own 80% of land.” (In 1910s Italy) (Pareto, 1919) Jérôme Kunegis Why Beyoncé Is More Popular Than Me Albert-Ludwigs-Universität Freiburg 4
  5. 5. A IR N F UJérôme Kunegis Why Beyoncé Is More Popular Than MeAlbert-Ludwigs-Universität Freiburg 5
  6. 6. 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 Why Beyoncé Is More Popular Than Me Albert-Ludwigs-Universität Freiburg 6
  7. 7. Degree distribution C(n) » n¡° Jérôme Kunegis Why Beyoncé Is More Popular Than Me Albert-Ludwigs-Universität Freiburg 7
  8. 8. TODO Jérôme Kunegis Why Beyoncé Is More Popular Than Me Albert-Ludwigs-Universität Freiburg 8
  9. 9. Which distribution is fairer?Flickr friendships OR Digg replies Jérôme Kunegis Why Beyoncé Is More Popular Than Me Albert-Ludwigs-Universität Freiburg 9
  10. 10. Lorenz Curve – Gini Coefficient Jérôme Kunegis Why Beyoncé Is More Popular Than Me Albert-Ludwigs-Universität Freiburg 10
  11. 11. Flickr Digg Jérôme Kunegis Why Beyoncé Is More Popular Than Me Albert-Ludwigs-Universität Freiburg 11
  12. 12. Perfect Power LawsJérôme Kunegis Why Beyoncé Is More Popular Than MeAlbert-Ludwigs-Universität Freiburg 12
  13. 13. (2) Entropy High entropy Low entropyJérôme Kunegis Why Beyoncé Is More Popular Than MeAlbert-Ludwigs-Universität Freiburg 13
  14. 14. @kunegis @beyonce @ststaab @noshir @barabasi Jérôme Kunegis Why Beyoncé Is More Popular Than Me Albert-Ludwigs-Universität Freiburg 14
  15. 15. EntropyJérôme Kunegis Why Beyoncé Is More Popular Than MeAlbert-Ludwigs-Universität Freiburg 15
  16. 16. max He = ln jVjJérôme Kunegis Why Beyoncé Is More Popular Than MeAlbert-Ludwigs-Universität Freiburg 16
  17. 17. Normalized EntropyJérôme Kunegis Why Beyoncé Is More Popular Than MeAlbert-Ludwigs-Universität Freiburg 17
  18. 18. Gini vs Entropy ½ = ¡0.71 p < 0.001Jérôme Kunegis Why Beyoncé Is More Popular Than MeAlbert-Ludwigs-Universität Freiburg 18
  19. 19. (3) Random Walks Diversity No diversityPret(L) large Pret(L) small Jérôme Kunegis Why Beyoncé Is More Popular Than Me Albert-Ludwigs-Universität Freiburg 19
  20. 20. Weighted Spectral DistributionPret(L) = §(i, j, . . . k) (d(i) d(j) . . . d(k)){1 = tr(NL) = § k ¸k Lwhere ¸k are eigenvalues of N = D{1/2 A D{1/2. Here: Use L = 4 and k · R Jérôme Kunegis Why Beyoncé Is More Popular Than Me Albert-Ludwigs-Universität Freiburg 20
  21. 21. Eigenvalues of NJérôme Kunegis Why Beyoncé Is More Popular Than MeAlbert-Ludwigs-Universität Freiburg 21
  22. 22. (4) ControllabilityDiversity No diversity (Liu, Slotine & Barabási 2011) Jérôme Kunegis Why Beyoncé Is More Popular Than Me Albert-Ludwigs-Universität Freiburg 22
  23. 23. Find a maximal directed 2-matching #Knobs needed = jVj { max jMj  Jérôme Kunegis Why Beyoncé Is More Popular Than Me Albert-Ludwigs-Universität Freiburg 23
  24. 24. Comparison Power Law Gini Norm. Entropy Random walks ControllabilityGenerality Power-law All networks All networks All networks All networksInterpretation Many (!) Economy Physical Simulation Control theoryRuntime Slow Fast Fast Medium FastCoverage d(u) ≥ dmin All All All All Jérôme Kunegis Why Beyoncé Is More Popular Than Me Albert-Ludwigs-Universität Freiburg 24
  25. 25. Network EvolutionJérôme Kunegis Why Beyoncé Is More Popular Than MeAlbert-Ludwigs-Universität Freiburg 25
  26. 26. “The Rich Get Richer”(Barabási & Albert 1999) Jérôme Kunegis Why Beyoncé Is More Popular Than Me Albert-Ludwigs-Universität Freiburg 26
  27. 27. “R an do m Wa lks Ar riv eL es sO ft e n”Jérôme Kunegis Why Beyoncé Is More Popular Than MeAlbert-Ludwigs-Universität Freiburg 27
  28. 28. “Ne two rks Get E as ier to C ont rol”Jérôme Kunegis Why Beyoncé Is More Popular Than MeAlbert-Ludwigs-Universität Freiburg 28
  29. 29. Experiments 20 networks from konect.uni-koblenz.de 9 authorship, 3 communication, 3 social, 3 interaction, 1 rating, 1 physicalMeasure Diversity No diversity Diversity decreasing trend increasingDiameter 12 8 0Gini coefficient 13 3 5Fractional rank 10 6 4Weighted spectral distribution 12 7 1Controllability 15 5 0 Jérôme Kunegis Why Beyoncé Is More Popular Than Me Albert-Ludwigs-Universität Freiburg 29
  30. 30. Thank YouJérôme Kunegis @kunegisWork in collaboration with Julia Preusse, Sergej Sizov, DamienFay & Felix SchwagereitWeST – Institute for Web Science and TechnologiesUniversity of Koblenz–Landau, Germanykonect.uni-koblenz.de Jérôme Kunegis Why Beyoncé Is More Popular Than Me Albert-Ludwigs-Universität Freiburg 30
  31. 31. ReferencesJ. Kunegis, S. Sizov, F. Schwagereit, D. Fay. Diversity Dynamics in OnlineNetworks. Proc. Conf. on Hypertext and Social Media, 2012.J. Kunegis, J. Preusse. Fairness on the Web: Alternatives to the Power Law.Proc. Web Science Conf., 2012.Y.-Y. Liu, J.-J. Slotine, A.-L. Barabási. Controllability of Complex Networks.Nature, 473:167–173, May 2011.J. Leskovec, J. Kleinberg, C. Faloutsos. Graph Evolution: Densification andShrinking Diameters. ACM Trans. Knowledge Discovery from Data, 1(1):1–40,2007.A.-L. Barabási, R. Albert. Emergence of Scaling in Random Networks.Science, 286(5439):509–512, 1999.V. Pareto. Manuale di economia politica con una introduzione alla scienzasociale (Manual of political economy). Milano : Societa Editrice Libraria, 1919. Jérôme Kunegis Why Beyoncé Is More Popular Than Me Albert-Ludwigs-Universität Freiburg 31
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