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International Symposium on the Science of Science
Library of Congress
March 21st 2016
Citation networks and the stories they tell
CarlT. Bergstrom
University of Washington
Jevin West Martin Rosvall
SciSIP
Jennifer Jacquet Jacob Foster Shelley Correll
Molly King DarilVilhena Ted Bergstrom
James Evans Ben Althouse Moritz Stefaner
Daniel Edler Ian Wesley-Smith Rodney Garrett
Michael Jensen Morton Bech Ralph Dandrea
Gregg Gordon
Eigenfactor.org/projects/well-­‐formed/	
  
Citation is a core institution of 
academic science, tracing the flow of
ideas over time.
The sum of all citations create a vast
network of more than a billion citations
among more than 100 million papers
Eigenfactor.org/projects/well-­‐formed/	
  
Every one of those citations represents
a careful decision by domain experts.
Eigenfactor.org/projects/well-­‐formed/	
  
The citation network of science holds a
wealth of information about how science
works, and how it can work better.
Eigenfactor.org/projects/well-­‐formed/	
  
How can we extract 
this information?
Eigenfactor.org/projects/well-­‐formed/	
  
The first step is to assemble the data. 

We have compiled citation networks 
from many sources:
How important is any particular
paper, or any particular journal,
in the network?
Mapequation.org	
  
Count incoming links
(Impact Factor)
Mapequation.org	
  
Count incoming links
(Impact Factor)
Use the whole network
(Eigenfactor)
Mapequation.org	
  
Important websites
are linked to by
important websites.
Important papers
are cited by 
important papers
Important journals
are cited by 
important journals
Eigenfactor algorithm
P = α H + (1 − α) a.eT
Matrix representing the
random walk over citations Probability of
not teleporting
Cross-citation Matrix
dictating the structure
of the citation network
Probability of teleporting
to completely new journal
weighted by the number
of articles in that journal
EF =100
Hπ
[Hπ]ii
∑
Leading eigenvector
of the random walk
matrix P.
Normalization
Bergstrom (2007);West et al (2010)
Applet coding: Daniel Edler
Mapequation.org	
  
The Eigenfactor Algorithm
Study, and publicize, the cost-
effectiveness of journal subscriptions
Eigenfactor.org	
  Bergstrom and Bergstrom 2004 PNAS
Study, and publicize, the cost-
effectiveness of open access publishing
Eigenfactor.org	
  
Ranking authors
“Author-level Eigenfactor
performs best in identifying
high-impact authors”
- Dunaiski et al.
J. Informetrics May 2016
West et al 2013 JASIST
Ranking articles: 
The Article-Level Eigenfactor (ALEF) Algorithm
Time
Older
papers
Newer
papers
Wesley-Smith et al 2016; West et al in prep.
Image Courtesy of Mark Newman
Small networks reveal structure
directly.
Dating network
in a Michigan
high school
Large networks could use some
assistance.
Yeast protein
interaction network
Ho et al. (2002) Nature
good maps simplify 
and highlight
relevant structures
Boston MTAGoogle maps
Network community detection

We want a modular description of a
weighted, directed network: 

Most flow on the network occurs within, 
not between, local modules.
Data
Compressing Finding patterns
If we can find a good code for describing flow on a
network, we will have solved the dual problem of
finding the important structures with respect to
that flow.
The map equation tells us the description
length for a particular modular structure
The map equation
We conclude that the infomap method by
Rosvall and Bergstrom is the best performing… 
Among other things, the method can be
applied to weighted and directed graphs as
well, with excellent performances, so it has a
large spectrum of potential applications.”
- Lancichinetti and Fortunato (2009)
“
Rosvall and Bergstrom (2008) PNAS
Althouse et al (2009) JASIST
“coverage” Impact factor
Althouse et al (2009) JASIST
1995 2004
1. Determine which structures
are statistically significant.
2. Visualize changes in those
structures.
Rosvall and Bergstrom (2010) 
PLoS One
The emergence of neuroscience
The map equation tells us the description
length for a particular hierarchical structure
The hierarchical map equation
Rosvall and Bergstrom (2011) 
PLoS One
Rosvall and Bergstrom (2011) PLoS One
Revealing hierarchical structure
Rosvall and Bergstrom (2011) PLoS One
Revealing hierarchical structure
Rosvall and Bergstrom (2011) PLoS One
Revealing hierarchical structure
Rosvall and Bergstrom (2011) PLoS One
Revealing hierarchical structure
Rosvall and Bergstrom (2011) 
PLoS One
Revealing hierarchical structure
Using hierarchical structure for
scholarly recommendation
West et al (2016) In press
http://babel.eigenfactor.org	
  
Using hierarchical structure for
scholarly recommendation
1920 1940 1960 1980 2000
0.100.150.200.250.30
percentageofwomen
What gender disparities still exist across academia?
first author
West et al. 2013 PLoS One
1920 1940 1960 1980 2000
0.100.150.200.250.30
percentageofwomen
What gender disparities remain 
in scholarly publishing?
last author
first author
West et al. 2013 PLoS One
Eigenfactor.org	
  
Self-citation rate by gender
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Women's and men's rates of self-citation
���� ���� ���� ���� ���� ����
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Based on  3 million papers from JSTOR
King et al. in prep.
Rates of rates of self-citation do make a
difference to impact metrics, particularly the h-index.
– Cameron et al 2016 Bioscience
Self-citations per authorship
”
“
King et al. in prep.
Citation metrics and the stories they tell

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Citation metrics and the stories they tell

  • 1. International Symposium on the Science of Science Library of Congress March 21st 2016 Citation networks and the stories they tell CarlT. Bergstrom University of Washington
  • 2. Jevin West Martin Rosvall SciSIP Jennifer Jacquet Jacob Foster Shelley Correll Molly King DarilVilhena Ted Bergstrom James Evans Ben Althouse Moritz Stefaner Daniel Edler Ian Wesley-Smith Rodney Garrett Michael Jensen Morton Bech Ralph Dandrea Gregg Gordon
  • 3. Eigenfactor.org/projects/well-­‐formed/   Citation is a core institution of academic science, tracing the flow of ideas over time.
  • 4. The sum of all citations create a vast network of more than a billion citations among more than 100 million papers Eigenfactor.org/projects/well-­‐formed/  
  • 5. Every one of those citations represents a careful decision by domain experts. Eigenfactor.org/projects/well-­‐formed/  
  • 6. The citation network of science holds a wealth of information about how science works, and how it can work better. Eigenfactor.org/projects/well-­‐formed/  
  • 7. How can we extract this information? Eigenfactor.org/projects/well-­‐formed/  
  • 8.
  • 9. The first step is to assemble the data. We have compiled citation networks from many sources:
  • 10. How important is any particular paper, or any particular journal, in the network? Mapequation.org  
  • 11. Count incoming links (Impact Factor) Mapequation.org  
  • 12. Count incoming links (Impact Factor) Use the whole network (Eigenfactor) Mapequation.org  
  • 13. Important websites are linked to by important websites.
  • 14. Important papers are cited by important papers Important journals are cited by important journals
  • 15. Eigenfactor algorithm P = α H + (1 − α) a.eT Matrix representing the random walk over citations Probability of not teleporting Cross-citation Matrix dictating the structure of the citation network Probability of teleporting to completely new journal weighted by the number of articles in that journal EF =100 Hπ [Hπ]ii ∑ Leading eigenvector of the random walk matrix P. Normalization Bergstrom (2007);West et al (2010)
  • 16. Applet coding: Daniel Edler Mapequation.org  
  • 18.
  • 19.
  • 20.
  • 21. Study, and publicize, the cost- effectiveness of journal subscriptions Eigenfactor.org  Bergstrom and Bergstrom 2004 PNAS
  • 22. Study, and publicize, the cost- effectiveness of open access publishing Eigenfactor.org  
  • 23. Ranking authors “Author-level Eigenfactor performs best in identifying high-impact authors” - Dunaiski et al. J. Informetrics May 2016 West et al 2013 JASIST
  • 24. Ranking articles: The Article-Level Eigenfactor (ALEF) Algorithm Time Older papers Newer papers Wesley-Smith et al 2016; West et al in prep.
  • 25.
  • 26. Image Courtesy of Mark Newman Small networks reveal structure directly. Dating network in a Michigan high school
  • 27. Large networks could use some assistance. Yeast protein interaction network Ho et al. (2002) Nature
  • 28. good maps simplify and highlight relevant structures Boston MTAGoogle maps
  • 29. Network community detection We want a modular description of a weighted, directed network: Most flow on the network occurs within, not between, local modules.
  • 30. Data Compressing Finding patterns If we can find a good code for describing flow on a network, we will have solved the dual problem of finding the important structures with respect to that flow.
  • 31. The map equation tells us the description length for a particular modular structure The map equation
  • 32. We conclude that the infomap method by Rosvall and Bergstrom is the best performing… Among other things, the method can be applied to weighted and directed graphs as well, with excellent performances, so it has a large spectrum of potential applications.” - Lancichinetti and Fortunato (2009) “
  • 33. Rosvall and Bergstrom (2008) PNAS
  • 34. Althouse et al (2009) JASIST
  • 37. 1. Determine which structures are statistically significant. 2. Visualize changes in those structures.
  • 38. Rosvall and Bergstrom (2010) PLoS One The emergence of neuroscience
  • 39. The map equation tells us the description length for a particular hierarchical structure The hierarchical map equation
  • 40. Rosvall and Bergstrom (2011) PLoS One
  • 41. Rosvall and Bergstrom (2011) PLoS One Revealing hierarchical structure
  • 42. Rosvall and Bergstrom (2011) PLoS One Revealing hierarchical structure
  • 43. Rosvall and Bergstrom (2011) PLoS One Revealing hierarchical structure
  • 44. Rosvall and Bergstrom (2011) PLoS One Revealing hierarchical structure
  • 45. Rosvall and Bergstrom (2011) PLoS One Revealing hierarchical structure
  • 46. Using hierarchical structure for scholarly recommendation West et al (2016) In press
  • 47. http://babel.eigenfactor.org   Using hierarchical structure for scholarly recommendation
  • 48. 1920 1940 1960 1980 2000 0.100.150.200.250.30 percentageofwomen What gender disparities still exist across academia? first author West et al. 2013 PLoS One
  • 49. 1920 1940 1960 1980 2000 0.100.150.200.250.30 percentageofwomen What gender disparities remain in scholarly publishing? last author first author West et al. 2013 PLoS One
  • 51. Self-citation rate by gender ● ● ● ●● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ●● ●● ●●●●●●● ● ● ● ● ● ●● ●●●●●●● ●●●●●● ● ●● ●● ● ●● ● ● ● ● ● ●●●● ● ●● ● ●● ● ●●● ● ● ● ● ●●● ●● ●● ● ●● ● ●● ● ●●●●●● ●●● ● ● ● ●●● ●● ● ● ● ●● Women's and men's rates of self-citation ���� ���� ���� ���� ���� ���� ���� ��� ��� ��� ��� ��� ��� ����-����� / ���������� Based on 3 million papers from JSTOR King et al. in prep.
  • 52. Rates of rates of self-citation do make a difference to impact metrics, particularly the h-index. – Cameron et al 2016 Bioscience Self-citations per authorship ” “ King et al. in prep.