The Complex Network of Wikipedia

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The Complex Network of Wikipedia
F. Colaiori, V. Servedio, G. Caldarelli,
AC physics dept., La Sapienza, Rome (Italy) D.
Donato, S. Leonardi computer science dept., La
Sapienza, Rome (Italy) L. Salete
Buriol computer science dept., University of
Porto Alegre, Rio Grande do Sul (Brazil)
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The Complex Network of Wikipedia
Network description Statistical analysis of
Wikipedia Model and interpretation
The Complex Network of Wikipedia
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La rete complessa di Wikipedia
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How does Wikipedia work?

• Thanks to the Wiki technology, a user can
• add new entries to the encyclopedia
• modify the content of existing entries
• modify their connections
• NB in the World Wide Web every user is
  responsible only for the out-degree of his web
  page.

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Nodes and edges in Wikipedia
Network edges are encyclopedia entries Edges
are citations between entries
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Statistical Properties
Entries number grows exponentially in time
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Statistical Properties
Preliminary results found by Voss and Zlatic show
that Wikipedia is indeed a complex network, with
power law degree distributions. J. Voss,
Proceedings of 10th International Conference of
the International Society for Scientometrics and
Informetrics, (Stockholm, Sweden), 2005. V.
Zlatic, M. Bozicevic, H. Stefancic, and M.
Domazet Phys. Rev. E 74, 016115 (2006)
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Degree distribution
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Preferential attachment
To detect the preferential attachment, we have
adopted the method introduced by Newman (2001)
one builds the histogram ?(k) of the degree of
vertices acquiring new edges at each time step t
weighing their contribution by a factor
n(k,t)/N(t), where N(t) is the number of nodes
at time t n(k,t) is the number of nodes with
degree k at time t If ?(k) has an approximatedly
linear behaviour, therefore perhaps we can
conclude that there is preferential attachment.
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Preferential attachment
Circles english Triangles portuguese Filled
in-degree White out-degree
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Lack of correlations (in-in)
english portuguese
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A model for Wikipedia

• At each time step one adds a node and M edges.
  The direction of edges is a random variable
• 1. with probability R1 the edge leaves the new
  node and points an existing node chosen with
  probability proportional to its in-degree.

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A model for Wikipedia

• At each time step one adds a node and M edges.
  The direction of edges is a random variable
• 2. with probability R2 the edge points the new
  node and leaves an existing node chosen with
  probability proportional to its out-degree.

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A model for Wikipedia

• At each time step one adds a node and M edges.
  The direction of edges is a random variable
• 3. with probability R3 1 R1 - R2 the edge
  points an existing node with probability
  proportional to its in-degree and leaves and
  leaves an existing node chosen with probability
  proportional to its out-degree.

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Parameters in real data

• The parameters have a physical meaning and can
  been measured on real data. In the english case,
  for instance, this yields
• R1 0.026, R2 0.091
• in the data we have, M 10

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Rate equation for in- e out-degree

• By approximating discrete time variation by
  derivativatives with respect to the continuous
  variable t, one can write and solve the following
  rate equations for the in- and out-degree
• dkin /dt (R1R3) kin t-1
• dkout /dt (R2R3) kout t-1

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Distribution of in- e out-degree

• By solving the rate equation, one obtains the
  time evolutions and, with little algebra, the
  distributions of the in- and out-degree

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Distribution of in- e out-degree

• Such distributions can be checked against real
  data, by plugging the real data coefficients
  R1,2,3 into the theoretical equations.

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Distribution of in- e out-degree
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Correlations

• The rate equations allow one to compute also the
  indegree-indegree correlations

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Lack of correlations
Model
model 0.5
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Naïf interpretation

• Hypothesis
• in-degree popularity
• out-degree quality
• If the probability of increasing the in-degree
  depends on the in-degree itself, it means that in
  Wikipedia popularity prevails over quality. As in
  the World Wide Web?

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Community structure

• Wikipedia displays a strong community structure

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Conclusions

• Wikipedia entries form a complex network with
  preferential attachment, power law distribution
  for both in- and out-degree and lack of
  correlations
• Preferential attachment explains the main
  statistical properties
• A naif interpretations would imply that the Wiki
  technology is not enough to provide a better
  dissemination of information with respect to the
  World Wide Web.
• More understanding is needed for the community
  structure.

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Thank You
Reference Preferential attachment in the growth
of social networks The internet encyclopedia
Wikipedia A.C., V. D. P. Servedio, F. Colaiori,
L. S. Buriol, D. Donato, S. Leonardi, and G.
Caldarelli Phys. Rev. E 74, 036116 (2006)
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