The Growth of
Wikipedia
Wikipedia
The growth of
Wikipedia
The dynamics of
the updates
The Growth of Wikipedia:
The evolution of
the hyperlinks
link and temporal analysis
Macroscopic
structure of the
Wikigraph
Preferential
D. Donato1,2
attachment in
the growth of
Joint work with: L.S. Buriol1 , L. Becchetti1 , A. Capocci3 ,
social networks
C. Castillo1,2 , F. Colaiori1 , G. Caldarelli1,3
Concluding
remarks
V.D.P.Servedio1,3
1. Universit` di Roma “La Sapienza” – Roma, Italy
a
2. Yahoo! Research Barcelona – Catalunya, Spain
3. Centro Studi e Ricerche E. Fermi – Roma, Italy

The Growth of
Wikipedia
Wikipedia
1
Wikipedia
The growth of
Wikipedia
The growth of Wikipedia
2
The dynamics of
the updates
The dynamics of the updates
The evolution of 3
the hyperlinks
Macroscopic
structure of the
The evolution of the hyperlinks
4
Wikigraph
Preferential
attachment in
the growth of
Macroscopic structure of the Wikigraph
5
social networks
Concluding
remarks
Preferential attachment in the growth of social networks
6
Concluding remarks
7

The Growth of
Wikipedia
Wikipedia
The growth of
Wikipedia
Wikipedia
1
The dynamics of
The growth of Wikipedia
2
the updates
The dynamics of the updates
3
The evolution of
the hyperlinks
The evolution of the hyperlinks
4
Macroscopic structure of the
5
Macroscopic
structure of the
Wikigraph
Wikigraph
Preferential attachment in the
6
Preferential
attachment in
growth of social networks
the growth of
Concluding remarks
7
social networks
Concluding
remarks

The Growth of
Wikipedia
Wikipedia
The growth of
Wikipedia
The dynamics of
the updates
The evolution of
the hyperlinks
Macroscopic
structure of the
Wikigraph
Preferential
attachment in
the growth of
social networks
Concluding
remarks

The Growth of
Wikipedia
Wikipedia
The growth of
Wikipedia
The dynamics of
the updates
The evolution of
the hyperlinks
Macroscopic
structure of the
Wikigraph
Preferential
attachment in
the growth of
social networks
Concluding
remarks

The Growth of
Wikipedia
Wikipedia
A Nature investigation aimed to find if Wikipedia is an
The growth of
authoritative source of information with respect to established
Wikipedia
The dynamics of
sources as Encyclopedia Britannica.
the updates
Among 42 entries tested, the difference in accuracy was not
The evolution of
the hyperlinks
particularly great:
Macroscopic
the average science entry in Wikipedia contained around
structure of the
Wikigraph
four inaccuracies;
Preferential
attachment in
the one in Britannica, about three.
the growth of
social networks
On the other hand the articles on Wikipedia are longer on
Concluding
average than those of Britannica. This accounts for a lower
remarks
rate of errors in Wikipedia (Nature 438, 900-901; 2005).

The Growth of
Why studying Wikipedia?
Wikipedia
sociological reasons: the encyclopedia collects pages written by a
Wikipedia
number of indipendent and heterogeneous
The growth of
Wikipedia
individuals. Each of them autonomously decides
The dynamics of
about the content of the articles with the only
the updates
constraint of a prefixed layout. The autonomy is a
The evolution of
common feature of the content creation in the Web.
the hyperlinks
The Wikipedia authors community is formed by
Macroscopic
structure of the
members whose only wish is to make available to the
Wikigraph
world concepts and topics that they consider
Preferential
attachment in
meaningful. In some sense, tracing the evolution of
the growth of
the Wikipedia subsets should mirror the develop of
social networks
significant trends within each linguistic community.
Concluding
remarks

The Growth of
Why studying Wikipedia?
Wikipedia
sociological reasons: the encyclopedia collects pages written by a
Wikipedia
number of indipendent and heterogeneous
The growth of
Wikipedia
individuals. Each of them autonomously decides
The dynamics of
about the content of the articles with the only
the updates
constraint of a prefixed layout. The autonomy is a
The evolution of
common feature of the content creation in the Web.
the hyperlinks
The Wikipedia authors community is formed by
Macroscopic
structure of the
members whose only wish is to make available to the
Wikigraph
world concepts and topics that they consider
Preferential
attachment in
meaningful. In some sense, tracing the evolution of
the growth of
the Wikipedia subsets should mirror the develop of
social networks
significant trends within each linguistic community.
Concluding
remarks
generation on time: Wikipedia provides time information associated
with nodes. Moreover, it provides old information:
time information for the creation and the
modifications for each page on the dataset.

The Growth of
Why studying Wikipedia?
Wikipedia
sociological reasons: the encyclopedia collects pages written by a
Wikipedia
number of indipendent and heterogeneous
The growth of
Wikipedia
individuals. Each of them autonomously decides
The dynamics of
about the content of the articles with the only
the updates
constraint of a prefixed layout. The autonomy is a
The evolution of
common feature of the content creation in the Web.
the hyperlinks
The Wikipedia authors community is formed by
Macroscopic
structure of the
members whose only wish is to make available to the
Wikigraph
world concepts and topics that they consider
Preferential
attachment in
meaningful. In some sense, tracing the evolution of
the growth of
the Wikipedia subsets should mirror the develop of
social networks
significant trends within each linguistic community.
Concluding
remarks
generation on time: Wikipedia provides time information associated
with nodes. Moreover, it provides old information:
time information for the creation and the
modifications for each page on the dataset.
independency of external links: Wikipedia articles link mainly to
articles on the same dataset.

The Growth of
Summarizing
Wikipedia
We have available all the history of growth, so that we
Wikipedia
can study the evolution
The growth of
Wikipedia
The dynamics of
the updates
The evolution of
the hyperlinks
Macroscopic
structure of the
Wikigraph
Preferential
attachment in
the growth of
social networks
Concluding
remarks

The Growth of
Summarizing
Wikipedia
We have available all the history of growth, so that we
Wikipedia
can study the evolution
The growth of
Wikipedia
large, compressed XML file containing information about
pages
The dynamics of
the updates
The evolution of
the hyperlinks
Macroscopic
structure of the
Wikigraph
Preferential
attachment in
the growth of
social networks
Concluding
remarks

The Growth of
Summarizing
Wikipedia
We have available all the history of growth, so that we
Wikipedia
can study the evolution
The growth of
Wikipedia
large, compressed XML file containing information about
pages
The dynamics of
the updates
inside each page, information about all the revisions the
The evolution of
page has undergo.
the hyperlinks
Macroscopic
structure of the
Wikigraph
Preferential
attachment in
the growth of
social networks
Concluding
remarks

The Growth of
Summarizing
Wikipedia
We have available all the history of growth, so that we
Wikipedia
can study the evolution
The growth of
Wikipedia
large, compressed XML file containing information about
pages
The dynamics of
the updates
inside each page, information about all the revisions the
The evolution of
page has undergo.
the hyperlinks
for each revision, the time stamp, author, editorial
Macroscopic
structure of the
comment and full text of the version of the page is
Wikigraph
available.
Preferential
attachment in
the growth of
social networks
Concluding
remarks

The Growth of
Summarizing
Wikipedia
We have available all the history of growth, so that we
Wikipedia
can study the evolution
The growth of
Wikipedia
large, compressed XML file containing information about
pages
The dynamics of
the updates
inside each page, information about all the revisions the
The evolution of
page has undergo.
the hyperlinks
for each revision, the time stamp, author, editorial
Macroscopic
structure of the
comment and full text of the version of the page is
Wikigraph
available.
Preferential
we generated 17 snapshots of the Web graph very 3
attachment in
the growth of
months, starting from January 1st, 2002 (14,247 articles)
social networks
until April 1st, 2006 (1,064,757 articles).
Concluding
remarks

The Growth of
Summarizing
Wikipedia
We have available all the history of growth, so that we
Wikipedia
can study the evolution
The growth of
Wikipedia
large, compressed XML file containing information about
pages
The dynamics of
the updates
inside each page, information about all the revisions the
The evolution of
page has undergo.
the hyperlinks
for each revision, the time stamp, author, editorial
Macroscopic
structure of the
comment and full text of the version of the page is
Wikigraph
available.
Preferential
we generated 17 snapshots of the Web graph very 3
attachment in
the growth of
months, starting from January 1st, 2002 (14,247 articles)
social networks
until April 1st, 2006 (1,064,757 articles).
Concluding
remarks
We have an example of a social network of huge size

The Growth of
Summarizing
Wikipedia
We have available all the history of growth, so that we
Wikipedia
can study the evolution
The growth of
Wikipedia
large, compressed XML file containing information about
pages
The dynamics of
the updates
inside each page, information about all the revisions the
The evolution of
page has undergo.
the hyperlinks
for each revision, the time stamp, author, editorial
Macroscopic
structure of the
comment and full text of the version of the page is
Wikigraph
available.
Preferential
we generated 17 snapshots of the Web graph very 3
attachment in
the growth of
months, starting from January 1st, 2002 (14,247 articles)
social networks
until April 1st, 2006 (1,064,757 articles).
Concluding
remarks
We have an example of a social network of huge size
We can compare the system produced by users of
different language, thereby measuring the effect of
different cultures.

The Growth of
Summarizing
Wikipedia
We have available all the history of growth, so that we
Wikipedia
can study the evolution
The growth of
Wikipedia
large, compressed XML file containing information about
pages
The dynamics of
the updates
inside each page, information about all the revisions the
The evolution of
page has undergo.
the hyperlinks
for each revision, the time stamp, author, editorial
Macroscopic
structure of the
comment and full text of the version of the page is
Wikigraph
available.
Preferential
we generated 17 snapshots of the Web graph very 3
attachment in
the growth of
months, starting from January 1st, 2002 (14,247 articles)
social networks
until April 1st, 2006 (1,064,757 articles).
Concluding
remarks
We have an example of a social network of huge size
We can compare the system produced by users of
different language, thereby measuring the effect of
different cultures.
We can study Wikipedia as a case study for the World
Wide Web [Buriol et al., 2005]

The Growth of
Wikipedia
Wikipedia
The growth of
Wikipedia
Wikipedia
1
The dynamics of
The growth of Wikipedia
2
the updates
The dynamics of the updates
3
The evolution of
the hyperlinks
The evolution of the hyperlinks
4
Macroscopic structure of the
5
Macroscopic
structure of the
Wikigraph
Wikigraph
Preferential attachment in the
6
Preferential
attachment in
growth of social networks
the growth of
Concluding remarks
7
social networks
Concluding
remarks

The Growth of
The growth of Wikipedia
Wikipedia
(a) Articles (b) Updates
Wikipedia
Number of updates (thousands)
Number of articles (thousands)
1200 9000
Actual Actual
The growth of 8000
6.2% monthly growth 11% monthly growth
1000
7000
Wikipedia 800 6000
5000
600
4000
The dynamics of 400 3000
the updates 2000
200
1000
0 0
The evolution of Jan Jan Jan Jan Jan Jan Jan Jan Jan Jan
’02 ’03 ’04 ’05 ’06 ’02 ’03 ’04 ’05 ’06
the hyperlinks Snapshot Snapshot
(c) Visitors (d) Editors
Macroscopic
structure of the
Wikigraph 35000 900
Number of users (thousands)
Actual Actual
Weekly Reach (millions)
800
30000 6.2% monthly growth 4.7% monthly growth
700
Preferential 25000
600
20000
attachment in 500
400
15000
the growth of 300
10000
200
social networks 5000 100
0 0
Concluding Jan Jan Jan Jan Jan Jan Jan Jan Jan
’03 ’04 ’05 ’06 ’02 ’03 ’04 ’05 ’06
remarks Snapshot Snapshot
In the last 3 years:
The number of articles is doubling itself in size every year, i.e. a
6.2% montly growth.
The number of updates has been growing at a rate of 11.3% per
month.
The number of different visitors and different editors have also been
growing at a fast peace.

The Growth of
Size of the articles
Wikipedia
Wikipedia
The growth of
Wikipedia
7.0
The dynamics of
Average page length [KB]
Created:
the updates
Before Jan’03
6.0
The evolution of
During 2003
the hyperlinks
5.0 During 2004
Macroscopic
During 2005
structure of the 4.0
Wikigraph
3.0
Preferential
attachment in
the growth of 2.0
social networks
1.0
Concluding
remarks Jan Jan Jan Jan
’03 ’04 ’05 ’06
Time
Individual articles have become longer, growing linearly during
the last two years at a rate of 1 KB of text every 6-8 months.

The Growth of
Wikipedia
Wikipedia
The growth of
Wikipedia
Wikipedia
1
The dynamics of
The growth of Wikipedia
2
the updates
The dynamics of the updates
3
The evolution of
the hyperlinks
The evolution of the hyperlinks
4
Macroscopic structure of the
5
Macroscopic
structure of the
Wikigraph
Wikigraph
Preferential attachment in the
6
Preferential
attachment in
growth of social networks
the growth of
Concluding remarks
7
social networks
Concluding
remarks

The Growth of
Pages Updates
Wikipedia
Wikipedia
The growth of
Wikipedia
106 106
The dynamics of
Actual Actual
the updates
105 105
Power−law (γ=2.07) Power−law (γ=2.07)
Number of Articles
Number of Articles
The evolution of
104 104
the hyperlinks
3
103
10
Macroscopic 2
102
10
structure of the
Wikigraph 101 101
100 100
Preferential
1 10 100 1000 10000 1 10 100 1000
attachment in
the growth of Number of Changes Number of Different Editors
social networks
The updates might be related to page views
Concluding
remarks

The Growth of
Pages Updates
Wikipedia
Wikipedia
The growth of
Wikipedia
106 106
The dynamics of
Actual Actual
the updates
105 105
Power−law (γ=2.07) Power−law (γ=2.07)
Number of Articles
Number of Articles
The evolution of
104 104
the hyperlinks
3
103
10
Macroscopic 2
102
10
structure of the
Wikigraph 101 101
100 100
Preferential
1 10 100 1000 10000 1 10 100 1000
attachment in
the growth of Number of Changes Number of Different Editors
social networks
The updates might be related to page views
Concluding
remarks
There is a prominent link to see the last 50 changes plus
the option to “watch” an article, to receive alerts when it
is changed

The Growth of
Editors’ behavior
Wikipedia
Wikipedia
7,5% of the articles have a single editor.
The growth of
Wikipedia
The dynamics of
the updates
The evolution of
the hyperlinks
Macroscopic
structure of the
Wikigraph
Preferential
attachment in
the growth of
social networks
Concluding
remarks

The Growth of
Editors’ behavior
Wikipedia
Wikipedia
7,5% of the articles have a single editor.
The growth of
Wikipedia
50% of the articles have more than 7 different editors.
The dynamics of
the updates
The evolution of
the hyperlinks
Macroscopic
structure of the
Wikigraph
Preferential
attachment in
the growth of
social networks
Concluding
remarks

The Growth of
Editors’ behavior
Wikipedia
Wikipedia
7,5% of the articles have a single editor.
The growth of
Wikipedia
50% of the articles have more than 7 different editors.
The dynamics of
the updates
5% of the articles have more than 50 different editors
The evolution of
the hyperlinks
Macroscopic
structure of the
Wikigraph
Preferential
attachment in
the growth of
social networks
Concluding
remarks

The Growth of
Editors’ behavior
Wikipedia
Wikipedia
7,5% of the articles have a single editor.
The growth of
Wikipedia
50% of the articles have more than 7 different editors.
The dynamics of
the updates
5% of the articles have more than 50 different editors
The evolution of
the hyperlinks
Fraction of Articles Updated
Macroscopic 30 1
structure of the 0.9
25
Updates per User
Wikigraph
0.8
20
0.7
Preferential
15
attachment in 0.6
10
the growth of 0.5
social networks 5 0.4
Concluding 0 0.3
remarks Jan Jan Jan Jan Jan Jan Jan Jan Jan Jan
’02 ’03 ’04 ’05 ’06 ’02 ’03 ’04 ’05 ’06
Time Time

The Growth of
Editors’ behavior
Wikipedia
Wikipedia
7,5% of the articles have a single editor.
The growth of
Wikipedia
50% of the articles have more than 7 different editors.
The dynamics of
the updates
5% of the articles have more than 50 different editors
The evolution of
the hyperlinks
Fraction of Articles Updated
Macroscopic 30 1
structure of the 0.9
25
Updates per User
Wikigraph
0.8
20
0.7
Preferential
15
attachment in 0.6
10
the growth of 0.5
social networks 5 0.4
Concluding 0 0.3
remarks Jan Jan Jan Jan Jan Jan Jan Jan Jan Jan
’02 ’03 ’04 ’05 ’06 ’02 ’03 ’04 ’05 ’06
Time Time
The fraction of articles that are updated is very high.
Over 80%of the articles are updated in the three-months
period we are considering for these snapshots.

The Growth of
Reverts
Wikipedia
Wikipedia
The growth of
Wikipedia
The dynamics of
the updates
The evolution of
the hyperlinks
Macroscopic
structure of the
Wikigraph
Preferential
attachment in
the growth of
social networks
Concluding
remarks

The Growth of
Reverts
Wikipedia
Wikipedia
The growth of
Wikipedia
The Reverts are one-click operations that take an article back
The dynamics of
the updates
to a previous version.
The evolution of
This is done mostly to fight vandalism.
the hyperlinks
Macroscopic
structure of the
7% 9%
Wikigraph
Double Reverts per Revert
8%
6%
Reverts per Update
7%
Preferential 5%
6%
attachment in
4% 5%
the growth of
4%
3%
social networks
3%
2%
2%
Concluding
1% 1%
remarks
0% 0%
Jan Jan Jan Jan Jan Jan Jan Jan Jan Jan
’02 ’03 ’04 ’05 ’06 ’02 ’03 ’04 ’05 ’06
Snapshot Snapshot

The Growth of
Clustering
Wikipedia
We clustered by the k-means algorithm the “update profile”
Wikipedia
of a set of pages using the euclidian distance among the
The growth of
Wikipedia
update vectors.
The dynamics of
the updates
Cluster 1 Cluster 4
The evolution of
1.0 1.0
the hyperlinks
Fraction of Updates
Fraction of Updates
0.8 0.8
Macroscopic
structure of the
0.6 0.6
Wikigraph
0.4 0.4
Preferential
attachment in
0.2 0.2
the growth of
social networks
0.0 0.0
Jan Jan Jan Jan Jan Jan
Concluding
’04 ’05 ’06 ’04 ’05 ’06
remarks
Cluster 2 Cluster 3
1.0 1.0
Fraction of Updates
Fraction of Updates
0.8 0.8
0.6 0.6
0.4 0.4
0.2 0.2
0.0 0.0

The Growth of
Wikipedia
Wikipedia
The growth of
Wikipedia
Wikipedia
1
The dynamics of
The growth of Wikipedia
2
the updates
The dynamics of the updates
3
The evolution of
the hyperlinks
The evolution of the hyperlinks
4
Macroscopic structure of the
5
Macroscopic
structure of the
Wikigraph
Wikigraph
Preferential attachment in the
6
Preferential
attachment in
growth of social networks
the growth of
Concluding remarks
7
social networks
Concluding
remarks

The Growth of
Degree Distribution
Wikipedia
The Degree shows fat tails that can be approximated by a
Wikipedia
power-law function of the kind P(K ) ∼ k1γ , for γ > 1. We
The growth of
Wikipedia
found γ = 2.00, similar to the value that has been observed in
The dynamics of
the indegree distribution of Web graphs (2.1)
the updates
[Broder et al., 2000, Donato et al., 2004].
The evolution of
the hyperlinks
Macroscopic
106 106
Actual
structure of the Actual
Power−law (γ=2.07)
105
Wikigraph 105 Power−law (γ=2.46)
Number of Articles
Number of Articles
104
Preferential 104
attachment in
3
103
10
the growth of
social networks
2
102
10
Concluding
1
101
10
remarks
0
100
10
1 10 100 1000 10000 1 10 100 1000 10000
Number of In−links Number of Out−links
The power-law exponent of the indegree has remained
remarkably constant even when the graph has grown
substantially in the studied period (from ≈14,000 articles to
≈1,000,000).

The Growth of
Average Outdegree
Wikipedia
The Wikipedia graph is becoming denser. During the last two
Wikipedia
and a half years, articles have grown from an average of 7
The growth of
Wikipedia
out-links per article to an average of 16 (on average one new
The dynamics of
reference every 100 days).
the updates
The evolution of
the hyperlinks
18
Actual
Macroscopic
16
structure of the 1 new link every 100 days
Wikigraph
14
Out−degree
Preferential
attachment in
12
the growth of
social networks
10
Concluding
8
remarks
6
4
Jan Jan Jan Jan Jan
’02 ’03 ’04 ’05 ’06
Time
This is a trend observed in other social networks by Leskovec et al.
[Leskovec et al., 2005].

The Growth of
PageRank
Wikipedia
Wikipedia
The tail of the distribution of PageRank for the usual parameter
The growth of
setting follows a power-law with exponent γ = 2.1
Wikipedia
[Donato et al., 2004].
The dynamics of
the updates
The evolution of
0.8
the hyperlinks
PageRank / In−Degree
0.7
Macroscopic
structure of the 0.6
Correlation
Wikigraph
0.5
Preferential 0.4
attachment in
0.3
the growth of
0.2
social networks
0.1
Concluding
remarks 0.0
Jan Jan Jan Jan Jan
’02 ’03 ’04 ’05 ’06
Time
The correlation between PageRank and indegree is very low in Web
graphs. Interestingly, in the Wikigraph this correlation has increased
in the last years, basically following the densification of the graph.

The Growth of
Wikipedia
Wikipedia
The growth of
Wikipedia
The dynamics of
the updates
The evolution of
Is the low PageRank/indegree correlation
the hyperlinks
Macroscopic
observed in Web graph a transient phenomenon?
structure of the
Wikigraph
Preferential
attachment in
the growth of
social networks
Concluding
remarks

The Growth of
Other microscopic measures
Wikipedia
Wikipedia
The growth of
0.30
Wikipedia
Clustering coefficient
0.28
The dynamics of
Edge reciprocity
0.26
the updates
0.24
Coefficient
The evolution of
the hyperlinks
0.22
0.20
Macroscopic
structure of the
0.18
Wikigraph
0.16
Preferential
0.14
attachment in
the growth of
0.12
social networks
0.10
Concluding
Jan Jan Jan Jan Jan
remarks
’02 ’03 ’04 ’05 ’06
Time
The Wikigraph seems to have stabilized in the last years
the average clustering coefficient is roughly 0.23

The Growth of
Other microscopic measures
Wikipedia
Wikipedia
The growth of
0.30
Wikipedia
Clustering coefficient
0.28
The dynamics of
Edge reciprocity
0.26
the updates
0.24
Coefficient
The evolution of
the hyperlinks
0.22
0.20
Macroscopic
structure of the
0.18
Wikigraph
0.16
Preferential
0.14
attachment in
the growth of
0.12
social networks
0.10
Concluding
Jan Jan Jan Jan Jan
remarks
’02 ’03 ’04 ’05 ’06
Time
The Wikigraph seems to have stabilized in the last years
the average clustering coefficient is roughly 0.23
the fraction of reciprocal edges is about about 0.13.

The Growth of
Assortativity
Wikipedia
Wikipedia
The growth of
Wikipedia
The dynamics of
the updates
The evolution of
the hyperlinks
Macroscopic
structure of the
Wikigraph
Preferential
attachment in
the growth of
social networks
Concluding
remarks
As regard the assortativity (as measured by the average
degree of the neighbours of a vertex with degree k) there is no
evidence of any assortative behaviour.

The Growth of
Wikipedia
Wikipedia
The growth of
Wikipedia
Wikipedia
1
The dynamics of
The growth of Wikipedia
2
the updates
The dynamics of the updates
3
The evolution of
the hyperlinks
The evolution of the hyperlinks
4
Macroscopic structure of the
5
Macroscopic
structure of the
Wikigraph
Wikigraph
Preferential attachment in the
6
Preferential
attachment in
growth of social networks
the growth of
Concluding remarks
7
social networks
Concluding
remarks

The Growth of
Connectivity
Wikipedia
The Wikigraph is almost entirely (weakly) connected. Over
Wikipedia
98.5% of the articles are connected to each other.
The growth of
Wikipedia
The dynamics of
70% 70%
the updates IN
60%
Size of IN and OUT
OUT
60%
The evolution of
Size of CORE
50%
the hyperlinks 50% 40%
Macroscopic 30%
40%
structure of the
20%
Wikigraph 30%
10%
Preferential 20% 0%
attachment in Jan Jan Jan Jan Jan Jan Jan Jan Jan Jan
the growth of ’02 ’03 ’04 ’05 ’06 ’02 ’03 ’04 ’05 ’06
Time Time
social networks
Concluding
the CORE component is getting larger.
remarks

The Growth of
Connectivity
Wikipedia
The Wikigraph is almost entirely (weakly) connected. Over
Wikipedia
98.5% of the articles are connected to each other.
The growth of
Wikipedia
The dynamics of
70% 70%
the updates IN
60%
Size of IN and OUT
OUT
60%
The evolution of
Size of CORE
50%
the hyperlinks 50% 40%
Macroscopic 30%
40%
structure of the
20%
Wikigraph 30%
10%
Preferential 20% 0%
attachment in Jan Jan Jan Jan Jan Jan Jan Jan Jan Jan
the growth of ’02 ’03 ’04 ’05 ’06 ’02 ’03 ’04 ’05 ’06
Time Time
social networks
Concluding
the CORE component is getting larger.
remarks
about 2/3 of the nodes belong to the larger strongly
connected component of the Wikigraph, which is larger
than was observed in 1999 in the Altavista
crawl [Broder et al., 2000] or in 2001 in the WebBase
crawl [Donato et al., 2004]

The Growth of
Connectivity
Wikipedia
Wikipedia
The growth of
Wikipedia
The dynamics of
the updates
The evolution of
the hyperlinks
Macroscopic
The increase of the size of the CORE has been mostly at
structure of the
Wikigraph
the expense of the OUT component
Preferential
attachment in
the growth of
social networks
Concluding
remarks

The Growth of
Migration of articles among the components
Wikipedia
We study the “movement” of articles among components of
Wikipedia
the different components of the Wikipedia graph,
The growth of
Wikipedia
following [Baeza-Yates and Poblete, 2004].
The dynamics of
the updates
The evolution of
the hyperlinks
Macroscopic
structure of the
Wikigraph
Preferential
attachment in
the growth of
social networks
Concluding
remarks
Interestingly, the CORE and OUT components are very stable, with
over 60% of the articles remaining in the same component after
three months. Also, these transition probabilities have remained
basically stable over different snapshots.

The Growth of
Wikipedia
Wikipedia
The growth of
Wikipedia
Wikipedia
1
The dynamics of
The growth of Wikipedia
2
the updates
The dynamics of the updates
3
The evolution of
the hyperlinks
The evolution of the hyperlinks
4
Macroscopic structure of the
5
Macroscopic
structure of the
Wikigraph
Wikigraph
Preferential attachment in the
6
Preferential
attachment in
growth of social networks
the growth of
Concluding remarks
7
social networks
Concluding
remarks

The Growth of
Preferential attachment hypothesis
Wikipedia
Given the history of growth one can verify the hypothesis of
Wikipedia
preferential attachment. This is done by means of the
The growth of
Wikipedia
histogram P(k) who gives the number of vertices (whose
The dynamics of
degree is k) acquiring new connections at time t.This is
the updates
quantity is weighted by the factor N(t)/n(k,t)
The evolution of
the hyperlinks
Macroscopic
structure of the
Wikigraph
Preferential
attachment in
the growth of
social networks
Concluding
remarks

The Growth of
Modelling
Wikipedia
Wikipedia
The growth of
From these data it seems that a model in the spirit of BA
Wikipedia
could reproduce most of the features of the system.
The dynamics of
the updates
Actually
The evolution of
the hyperlinks
This network is oriented.
Macroscopic
structure of the
Wikigraph
Preferential
attachment in
the growth of
social networks
Concluding
remarks

The Growth of
Modelling
Wikipedia
Wikipedia
The growth of
From these data it seems that a model in the spirit of BA
Wikipedia
could reproduce most of the features of the system.
The dynamics of
the updates
Actually
The evolution of
the hyperlinks
This network is oriented.
Macroscopic
structure of the
The preferential attachment in Wikipedia has a
Wikigraph
somewhat different nature. Here, most of the times, the
Preferential
attachment in
edges are added between existing vertices differently from
the growth of
social networks
the BA model. For instance, in the English version of
Concluding
Wikipedia a largely dominant fraction 0.883 of new edges
remarks
is created between two existing pages, while a smaller
fraction of edges points or leaves a newly added vertex
(0.026 and 0.091 respectively).

The Growth of
Modelling
Wikipedia
We introduced an evolution rule, similar to other models of
Wikipedia
rewiring already considered. At each time step we make a
The growth of
Wikipedia
move
The dynamics of
A vertex is added to the network. It is connected to the
the updates
The evolution of
existing vertices by M oriented edges.
the hyperlinks
Macroscopic
structure of the
Wikigraph
Preferential
attachment in
the growth of
social networks
Concluding
remarks

The Growth of
Modelling
Wikipedia
We introduced an evolution rule, similar to other models of
Wikipedia
rewiring already considered. At each time step we make a
The growth of
Wikipedia
move
The dynamics of
A vertex is added to the network. It is connected to the
the updates
The evolution of
existing vertices by M oriented edges.
the hyperlinks
with probability R1 the edge leaves the new vertex
Macroscopic
structure of the
pointing to an existing one chosen with probability
Wikigraph
proportional to its indegree;
Preferential
attachment in
the growth of
social networks
Concluding
remarks

The Growth of
Modelling
Wikipedia
We introduced an evolution rule, similar to other models of
Wikipedia
rewiring already considered. At each time step we make a
The growth of
Wikipedia
move
The dynamics of
A vertex is added to the network. It is connected to the
the updates
The evolution of
existing vertices by M oriented edges.
the hyperlinks
with probability R1 the edge leaves the new vertex
Macroscopic
structure of the
pointing to an existing one chosen with probability
Wikigraph
proportional to its indegree;
Preferential
attachment in
the growth of
with probability R2, the edge points to the new vertex,
social networks
and the source vertex is chosen with probability
Concluding
remarks
proportional to its outdegree.

The Growth of
Modelling
Wikipedia
We introduced an evolution rule, similar to other models of
Wikipedia
rewiring already considered. At each time step we make a
The growth of
Wikipedia
move
The dynamics of
A vertex is added to the network. It is connected to the
the updates
The evolution of
existing vertices by M oriented edges.
the hyperlinks
with probability R1 the edge leaves the new vertex
Macroscopic
structure of the
pointing to an existing one chosen with probability
Wikigraph
proportional to its indegree;
Preferential
attachment in
the growth of
with probability R2, the edge points to the new vertex,
social networks
and the source vertex is chosen with probability
Concluding
remarks
proportional to its outdegree.
Finally, with probability R3 = 1 - R1 - R2 the edge is
added between existing vertices: the source vertex is
chosen with probability proportional to the outdegree,
while the destination vertex is chosen with probability
proportional to the indegree.

The Growth of
Modelling
Wikipedia
Wikipedia
The growth of
Wikipedia
The model can be solved analytically:
The dynamics of
the updates
The evolution of
the hyperlinks
Macroscopic
structure of the
Wikigraph
Preferential
attachment in
the growth of
social networks
Concluding
remarks
We can use for the model the empirical values of R1=0.026
R2=0.091 R3=0.883 Already measured for the English version
of Wikigraph

The Growth of
Wikipedia
Wikipedia
The growth of
Wikipedia
Wikipedia
1
The dynamics of
The growth of Wikipedia
2
the updates
The dynamics of the updates
3
The evolution of
the hyperlinks
The evolution of the hyperlinks
4
Macroscopic structure of the
5
Macroscopic
structure of the
Wikigraph
Wikigraph
Preferential attachment in the
6
Preferential
attachment in
growth of social networks
the growth of
Concluding remarks
7
social networks
Concluding
remarks

The Growth of
Signs of transient regime (growth)
Wikipedia
Wikipedia
The growth of
Wikipedia
The dynamics of
the updates
The number of articles, updates, visitors and editors is
The evolution of
still growing exponentially.
the hyperlinks
Macroscopic
structure of the
Wikigraph
Preferential
attachment in
the growth of
social networks
Concluding
remarks

The Growth of
Signs of transient regime (growth)
Wikipedia
Wikipedia
The growth of
Wikipedia
The dynamics of
the updates
The number of articles, updates, visitors and editors is
The evolution of
still growing exponentially.
the hyperlinks
Macroscopic
The size of articles is still growing linearly.
structure of the
Wikigraph
Preferential
attachment in
the growth of
social networks
Concluding
remarks

The Growth of
Signs of transient regime (growth)
Wikipedia
Wikipedia
The growth of
Wikipedia
The dynamics of
the updates
The number of articles, updates, visitors and editors is
The evolution of
still growing exponentially.
the hyperlinks
Macroscopic
The size of articles is still growing linearly.
structure of the
Wikigraph
The number of links per article is also growing linearly,
Preferential
slowly than the amount of text.
attachment in
the growth of
social networks
Concluding
remarks

The Growth of
Signs of transient regime (growth)
Wikipedia
Wikipedia
The growth of
Wikipedia
The dynamics of
the updates
The number of articles, updates, visitors and editors is
The evolution of
still growing exponentially.
the hyperlinks
Macroscopic
The size of articles is still growing linearly.
structure of the
Wikigraph
The number of links per article is also growing linearly,
Preferential
slowly than the amount of text.
attachment in
the growth of
The number of reverts is growing slowly, which may
social networks
Concluding
signal more vandalism, but the number of double reverts
remarks
(revert wars) has stabilized.

The Growth of
Signs of permanent regime (maturity)
Wikipedia
Wikipedia
The growth of
There is a clear power-law distribution of the indegree
Wikipedia
The dynamics of
and outdegree.
the updates
The evolution of
the hyperlinks
Macroscopic
structure of the
Wikigraph
Preferential
attachment in
the growth of
social networks
Concluding
remarks

The Growth of
Signs of permanent regime (maturity)
Wikipedia
Wikipedia
The growth of
There is a clear power-law distribution of the indegree
Wikipedia
The dynamics of
and outdegree.
the updates
The average edits per user has been mostly constant in
The evolution of
the hyperlinks
the last two years.
Macroscopic
structure of the
Wikigraph
Preferential
attachment in
the growth of
social networks
Concluding
remarks

The Growth of
Signs of permanent regime (maturity)
Wikipedia
Wikipedia
The growth of
There is a clear power-law distribution of the indegree
Wikipedia
The dynamics of
and outdegree.
the updates
The average edits per user has been mostly constant in
The evolution of
the hyperlinks
the last two years.
Macroscopic
structure of the
There is a high correlation between PageRank and
Wikigraph
indegree, indicating that the microscopic connectivity of
Preferential
attachment in
the encyclopedia resembles its mesoscopic
the growth of
social networks
Concluding
remarks

The Growth of
Signs of permanent regime (maturity)
Wikipedia
Wikipedia
The growth of
There is a clear power-law distribution of the indegree
Wikipedia
The dynamics of
and outdegree.
the updates
The average edits per user has been mostly constant in
The evolution of
the hyperlinks
the last two years.
Macroscopic
structure of the
There is a high correlation between PageRank and
Wikigraph
indegree, indicating that the microscopic connectivity of
Preferential
attachment in
the encyclopedia resembles its mesoscopic
the growth of
social networks
The clustering coefficient and edge reciprocity of links
Concluding
have remained basically constant during the last two
remarks
years.

The Growth of
Signs of permanent regime (maturity)
Wikipedia
Wikipedia
The growth of
There is a clear power-law distribution of the indegree
Wikipedia
The dynamics of
and outdegree.
the updates
The average edits per user has been mostly constant in
The evolution of
the hyperlinks
the last two years.
Macroscopic
structure of the
There is a high correlation between PageRank and
Wikigraph
indegree, indicating that the microscopic connectivity of
Preferential
attachment in
the encyclopedia resembles its mesoscopic
the growth of
social networks
The clustering coefficient and edge reciprocity of links
Concluding
have remained basically constant during the last two
remarks
years.
Over 2/3 of the articles belong now to the larger strongly
connected component.

The Growth of
Wikipedia
Wikipedia
Thank you!
The growth of
Wikipedia
The dynamics of
the updates
The evolution of
the hyperlinks
Macroscopic
structure of the
Wikigraph
Preferential
attachment in
the growth of
social networks
Concluding
remarks

The Growth of
Wikipedia
Wikipedia
Thank you!
The growth of
Wikipedia
The dynamics of
the updates
The evolution of
the hyperlinks
Macroscopic
structure of the
Wikigraph
Preferential
attachment in
the growth of
social networks
Concluding
remarks

The Growth of
Wikipedia
Baeza-Yates, R. and Poblete, B. (2004).
Dynamics of the chilean web structure.
Wikipedia
In Proc. of the 3rd WebDyn.
The growth of
Wikipedia
Broder, A., Kumar, R., Maghoul, F., Raghavan, P.,
The dynamics of
the updates
Rajagopalan, S., Stata, R., Tomkins, A., and Wiener, J.
The evolution of
(2000).
the hyperlinks
Graph structure in the web: Experiments and models.
Macroscopic
structure of the
In Proc. of the 9th WWW, pages 309–320. ACM Press.
Wikigraph
Preferential
Buriol, L. S., Donato, D., Leonardi, S., and Millozzi, S. (2005).
attachment in
the growth of
social networks
Link and temporal analysis of wikigraphs.
Concluding
Technical report, DELIS – Dynamically Evolving, Large-Scale
remarks
Information Systems.
Donato, D., Laura, L., Leonardi, S., and Millozzi, S. (2004).
Large scale properties of the webgraph.
European Physical Journal B, 38:239–243.

The Growth of
Wikipedia
Wikipedia
The growth of
Wikipedia
The dynamics of
the updates
Leskovec, J., Kleinberg, J., and Faloutsos, C. (2005).
The evolution of
the hyperlinks
Graphs over time: densification laws, shrinking diameters and
Macroscopic
possible explanations.
structure of the
Wikigraph
In Proc. of the 11th KDD, pages 177–187. ACM Press.
Preferential
attachment in
the growth of
social networks
Concluding
remarks