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A Locality Model of the Evolution of Blog Networks

A Locality Model of the Evolution of Blog Networks. Blog Networks. Increasingly important communication forum Size Ease of communication Global Can represent as a graph LiveJournal Blog network 15+ million worldwide users 500,000 Russian users Very dynamic. Goal.

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A Locality Model of the Evolution of Blog Networks

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  1. A Locality Model of the Evolution of Blog Networks

  2. Blog Networks • Increasingly important communication forum • Size • Ease of communication • Global • Can represent as a graph • LiveJournal Blog network • 15+ million worldwide users • 500,000 Russian users • Very dynamic IEEE ISI 2008, Taipei

  3. Goal • Social Network: directed graph • Evolution: sequence of directed graphs We wish to model evolution IEEE ISI 2008, Taipei

  4. B B B B B B A A A A A A C C C C C C Why Model Evolution • Contagion processes are different on static vs. dynamic networks. • Information flow on the blogs • Rumors • Advertising and viral marketing • High value nodes in contagion processes Static Dynamic IEEE ISI 2008, Taipei

  5. Growth vs. Evolution • Growth • Add new nodes • Links static • Given node out degrees • Model specifies where to attach upon node arrival • eg. growth of internet • Preferential attachment • Power-law degree distributions • Evolution • Node set static • Links change • Given node out degrees • Model specifies where to re-attach at each time step • eg. evolution of blog-network communications • Preferential attachment? • Power-law degree distributions? IEEE ISI 2008, Taipei

  6. Blog-Networks are very Dynamic 150,000 users each week 500,000 communications each week 350,000 are new 70% edges are new each week IEEE ISI 2008, Taipei

  7. Stability: the in-degree distribution Other stable statistics: power-law exponent; clustering coef; av. path length; largest component; community structure;… Stability despite extreme communication dynamics IEEE ISI 2008, Taipei

  8. Modeling Evolution of Blogs C C A A B B J J D D E E F F H H G G BlogNetwork(t) BlogNetwork(t+1) MODEL IEEE ISI 2008, Taipei

  9. Testing Models • Iterate model to stability • Observed stable statistics should be stable in the model • In-degree distribution • Values of stable statistics should match observed values • Stable power-law in-degree distribution resulting from evolution IEEE ISI 2008, Taipei

  10. Global Preferential Re-Attachment C A B J D Power Houses Appear E F H G BlogNetwork(t) BlogNetwork(t+1) GPRA IEEE ISI 2008, Taipei

  11. C A B J D E F H G General Locality Based Model 1. Given: • BlogNetwork at previous time step • Node-Outdegrees IEEE ISI 2008, Taipei

  12. C A B J D E F H G General Locality Based Model 2. Every node determines its “social” locality LOCALITY IEEE ISI 2008, Taipei

  13. General Locality Based Model 3. Every node re-attaches its edges inside its “social” locality. C A B J D E F ATTACHMENT H G IEEE ISI 2008, Taipei

  14. Locality and Attachment Attachment Mechanism Uniformly random Preferential Attachment Erdos-Reyni random graph GPRA Global Locally random neighborhoods Local-PRA Locality 2-Neighborhood Community (Union of Social Groups*) Locally random communities Community-PRA *Social group = cluster [Baumes, Goldberg, Magdon-Ismail 2005] IEEE ISI 2008, Taipei

  15. Results Model Errors Significance: 0.038 IEEE ISI 2008, Taipei

  16. Summing Up • Modeling blog dynamics is important for information and contagion diffusion. • Simple GPRA does not reproduce stable power-law distributions • Community-PRA gives best model • Other stable statistics for improving models: • Cluster coefficient • Community structure • Fat tail • Path lengths IEEE ISI 2008, Taipei

  17. Thank You! http://www.cs.rpi.edu/~magdon SHAMELESS ADVERTISEMENT ADN 2008: International Workshop on Analysis of Dynamic Networks (in conjunction with IEEE ICDM 2008) http://compbio.cs.uic.edu/adn-icdm08/ IEEE ISI 2008, Taipei

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