Measurement and Evolution of Online Social Networks

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					        Measurement and Evolution of
          Online Social Networks
                           Review of paper by Ophir Gaathon
               Analysis of Social Information Networks

             COMS 6998-2, Spring 2011, Topic #1: April 7th
                       Columbia University

                                       Focus
Leskovec et al. Graphs over time: densification laws, shrinking diameters and possible
                                explanations.(2005)

                                        Space
      Mislove et al. Measurement and analysis of online social networks. (2007)
           Leskovec et al. Microscopic evolution of social networks (2008)
                 Kumar et al. Structure and evolution of online social
                                  networks. (2010)
         What is a social interaction?
                                       Family
                                                  Anonymous

                                                                              Friends
                       Work              Life                                 of Friends
                                                                              of Friends
                          Co-Workers
                                                          Friends
                                        Friends          of Friends




 Online space

There are different forms/contexts/spheres of interaction on different platforms/networks

               What are the rules of interaction that every network has?
    What are the risk and rewords for linking or disconnecting in any given network?
What kind of social interaction
                Facebook
    platform is Linkedin ?
                  Twiter
                  Flickr
                 youtube
                               Percent of global Internet
                               users who visit the site




* Google as a weekday signal
               The Rules
• Youtube, flickr – „just post it‟
• Facebook – befriend me
• Twitter- I follow you; you follow me
  (according to center of gravity)

• Scientific Papers – you must reference
  prior work
• Patents – you must identify prior art
                 How do real graphs evolve over time?
      What are “normal” growth patterns in social, technological, and
                         information networks?

(A) Constant average degree            (A‟) Empirical observation:
   assumption: The average node            Densification power laws: The
                                           networks are becoming denser over
   degree in the network remains           time, with the average degree
   constant over time. (Or                 increasing (and hence with the
   equivalently, the number of             number of edges growing super-
   edges grows linearly in the             linearly in the number of nodes).
                                           Moreover, the densification follows a
   number of nodes.)                       power-law pattern.
(B) Slowly growing diameter            (B‟) Empirical observation: Shrinking
   assumption: The diameter is a           diameters: The effective diameter
   slowly growing function of the          is, in many cases, actually
                                           decreasing as the network grows.
   network size, as in “small world”
   graphs.
                                     arXiv
    • started in 1991 as a repository for preprints in physics and later
      expanded to include astronomy, mathematics, computer
      science, nonlinear science, quantitative biology and, most recently,
      statistics.[2].
    • In many fields of mathematics and physics, almost all scientific
      papers are placed on the arXiv.
    • On October 2008, arXiv.org passed the 500,000 article milestone.
    • roughly five thousand new article added every month.[1]
    • arXiv is not peer reviewed, although there are a collection of
      moderators for each area review the submissions and may
      recategorize any that are deemed off-topic.

    • High Energy Physics - Theory (since Aug 1991)
    • High Energy Physics - Phenomenology (since Mar 1992)
    • Astrophysics (since Apr 1992)



http://en.wikipedia.org/wiki/ArXiv
• Is the densification a boundary (off-field)
  limitation of the dataset?
• How can we account for links that are not in the
  network? Example: Facebook friends that are
  actually friends will call each other and send
  email off Facebook network.
• Will this have any effect to our view of the
  network density ? – not a sampling question
We are all connected
                                                                          Map of Science-
                                                                          Different fields are connected*




http://www.lanl.gov/news/index.php/fuseaction/home.story/story_id/15960
What is the portion of links that are to
            outside-nodes?

    How complete is the dataset?
      What are the implications of citing
      more and more papers & patents?
    • Every paper can only contain a finite number of
      references – is a bounded problem?
    • More references to other patents - Patents become
      longer with longer prosecution time and longer office
      actions




http://www.patentlyo.com/patent/patent_prosecution/
http://soshable.com/twitter-vs-facebook-across-the-web/
Percent of global Internet
users who visit the site
       Derek John de Solla Price
• studies of the exponential growth of science and the half-life of
  scientific literature; together with the formulation of Price's Law,
  namely that 25% of scientific authors are responsible for 75% of
  published papers (Price 1963);
• quantitative studies of the network of citations between scientific
  papers (Price 1965), including the discovery that both the in- and
  out-degrees of a citation network have power-law distributions,
  making this the first published example of a scale-free network;
• a mathematical theory of the growth of citation networks, based on
  what would now be called a preferential attachment process (Price
  1976);[2]
• an analysis of the Antikythera mechanism, an ancient Greek
  clockwork calculator (Price 1959, 1974).

				
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posted:9/5/2011
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