Santo Fortunato Universality of citation distributions The World - PowerPoint PPT Presentation

Santo Fortunato

• Universality of citation distributions • The World Citation Network • The World Collaboration Network • Citation boosts: the rise of Nobel laureates

Citation statistics Source of data Papers are classified in 172 scientific disciplines (from Acoustics to Zoology ) ‏

Dependence on field (ISI category)!

Could c 0 be the reason of the discrepancy? F. Radicchi, S.F. and C. Castellano, Proc. Natl. Acad. Sci. USA 105, 17268 (2008)

F. Radicchi, S.F. and C. Castellano, Proc. Natl. Acad. Sci. USA 105, 17268 (2008)

The universal distribution is stable in time!

Fitting the universal distribution

¡ ¡ ¡ Summary I • The distribution of the number of citations of papers in the same discipline, normalized by the average citation score, is universal! • It is possible to compare the impact of papers in different disciplines in an objective way • Relative citation indicators could lead to more reliable indices of individual performance than, say, the H-index

¡ ¡ ¡ The World Citation Network Goal: studying the geographic distributions and correlations of citation flows Data: Thomson Reuters (ISI Web of Science) database, from 2003 until 2010

¡ ¡ ¡ Author affiliations

¡ ¡ ¡ Author affiliations Finland, UK, USA, USA, Hungary Espoo, Oxford, South Bend, Cambridge (MA), Budapest

¡ ¡ ¡ Citation networks Citations are split among the cited authors, and then they are attributed to the countries/cities of the authors

¡ ¡ ¡ Collaboration networks Paper Affiliation 1 1/3 Affiliation 2 1/3 1/3 Affiliation 3 Collaboration links receive a weight of 2/[n(n-1)], where n is the number of different countries/cities involved in the paper

¡ ¡ ¡ Summary of statistics

World publications: density- equalizing map 10 6 70 � 50 � 10 5 30 � 10 4 N contribution 10 � 10 3 − 10 � 10 2 − 30 � 10 1 − 50 � − 70 � 10 0 − 180 � − 150 � − 120 � − 90 � − 60 � − 30 � 0 � 30 � 60 � 90 � 120 � 150 � 180 � M. Gastner, M. E. J. Newman, Proc. Natl. Acad. Sci. U.S.A. 101, 7499 (2004)

¡ ¡ ¡ World citations: map

World citations: density- equalizing map M. Gastner, M. E. J. Newman, Proc. Natl. Acad. Sci. U.S.A. 101, 7499 (2004)

World citation averages

World citation distributions

City-level citation distributions 10 0 α ∼ -1.41 α ∼ -1.40 10 − 2 P ( N Pub ) P ( N Cite ) ) 10 − 4 P ( w Cite ij s in 10 − 6 10 − 8 w ij w ii 10 − 10 10 0 10 2 10 4 10 6 10 − 2 10 0 10 2 10 4 10 6 10 0 10 2 10 4 N Pub N Cite w Cite ij

City citation statistics: correlations 10 0 10 6 α ∼ 1.00 10 4 10 − 1 α ∼ 0.12 10 4 10 2 w Cite α ∼ 0.87 s in 10 − 2 j ij 10 0 10 2 α ∼ 2.20 10 − 3 10 − 2 10 0 10 − 4 10 − 4 10 6 10 0 10 1 10 2 10 3 10 4 10 3 10 6 10 9 10 12 k in s out s in j i j

City-level collaborations: distributions and correlations 10 0 1 . 0 10 0 0 . 8 10 − 1 10 − 2 ij ) 0 . 6 ii /s i P c ( w Col 10 − 2 w Col 0 . 4 10 − 4 10 − 3 0 . 2 w ij w ii 10 − 6 0 . 0 10 − 4 10 0 10 1 10 2 10 3 10 4 10 5 10 − 2 10 0 10 2 10 4 s i w Col ij 10 4 α ∼ 0.97 10 4 10 2 α ∼ 0.16 w Col 10 2 10 0 s i ij 10 − 2 10 0 α ∼ 1.61 10 − 4 10 8 10 10 10 0 10 2 10 4 10 2 10 4 10 6 s i s j k i

Citation vs collaborations 10 0 10 6 10 4 10 − 1 + w cite 10 4 ji 10 2 α ∼ 0.82 10 − 2 10 2 w cite 10 0 α ∼ 1.06 ij 10 − 3 10 0 10 − 2 10 − 2 10 − 4 10 0 10 2 10 4 10 − 2 10 0 10 2 10 4 w col w col ij ij

Gravity law w ij ∝ s out s in i j d α ij

Gravity law: citations

Gravity law: collaborations

Gravity law: link probability vs distance

Cites vs number of authors (I) 10 4 10 3 h n c i 10 2 10 1 10 0 5 10 15 20 N Authors

Cites vs number of authors (II) 10 0 10 − 1 h n c i 10 − 2 10 − 3 10 − 4 2 4 6 8 10 N Cities

Cites vs number of authors (III) h n c i 2 4 6 8 10 N Countries

Cites vs number of authors: summary

Funding vs citations 10 6 10 5 N pub 10 4 10 3 α ∼ 0.90 α ∼ 0.96 10 2 10 1 10 7 10 6 N cite 10 5 10 4 α ∼ 0.99 α ∼ 0.98 10 3 10 2 10 0 10 1 10 2 10 3 10 4 10 5 10 6 10 1 10 2 10 3 10 4 10 5 10 6 R&D expense (M $ ) N researcher

Funding vs citations 14 120,000 $ 120,000 $ PA CH 12 IS DK NL SC US SE DE BE 10 GB CR FI AT FR CA NO IT AU h n c i IE 8 ES NZ World average citation HU JP PY CL SG EC EE PT UY MZ SN AR LU GR PH CZ MG GT 6 MT ZA TH MX CO PL LV KR SI SK CN BR MD LK BG HR ET BN IN MA CY RU 4 LS MK LT TR KW EG UA IR RS RO MY TN PK DZ BA 2 10 3 10 4 10 5 10 6 R&D expense / N researcher ( $ )

bias for country i = Funding vs citations Bias Bias Bias Bias Bias 0 . 0 0 . 5 1 . 0 1 . 5 2 . 0 0 . 0 0 . 5 1 . 0 1 . 5 2 . 0 0 . 0 0 . 5 1 . 0 1 . 5 2 . 0 2 . 5 0 . 0 0 . 5 1 . 0 1 . 5 2 . 0 2 . 5 0 . 4 0 . 7 1 . 0 1 . 3 1 . 6 United States China United Kingdom Japan Germany Canada France Italy India South Korea Spain Australia Russia Netherlands Taiwan Brazil Turkey P Sweden Switzerland Poland N set Belgium i N set Israel Iran i Greece Top 100 SocialScience Journals Denmark Top 100 Science Journals Finland i Top 10% cited papers Austria Top 1% cited papers Mexico Total Citations Singapore Norway Czech Republic Portugal × South Africa New Zealand Argentina Ireland P Hungary Egypt N i Romania i N i Ukraine

¡ ¡ ¡ Summary II • Geography plays an important role in the dynamic of citation and collaboration patterns • The strengths of citation flows and/or collaborations obey gravity laws, i.e. they display a power law decay with distance • The number of citations of a paper increases with the number of authors, affiliations and countries • There is a threshold effect in the relationship between research funding and citations: below 120,000 $ per researcher the average number of cites of papers of a country stays below the world average.

How to get more citations? • Write papers with many people • Get good neighbors • Do international collaborations • Get more funding!

Nobel boosts … Goal: studying the occurrence and effects of groundbreaking papers on scientific careers Focus: Nobel Prize Laureates Data: ISI Web of Science citations of papers of 124 Nobel Prize Laureates in the last two decades (1990-2009) A. Mazloumian, Y.-H. Eom, D. Helbing, S. Lozano, S. F., PLoS One 6(5), e18975 (2011)

The boost factor Principle: comparing the citation rates of articles before and after time t of papers published before t R <t,w = Average number of citations per paper and year received in the period [t-w+1, t] R >t,w = Average number of citations per paper and year received in the period [t+1, t+w] R w ( t ) = R >t,w R <t,w

The boost factor MR Capecchi JC Mather a b r o t c a f t s RY Tsien RB Myerson o o B c d Year

The boost factor vs standard indicators MR Capecchi JC Mather Normalized index value a b e z i s t c e RY Tsien RB Myerson ff E Boost factor h-index Avg. Citations per paper c d Cumulative citations Year t

¡ ¡ ¡ Summary III • Groundbreaking scientific papers have a boosting effect on previous publications of their authors, even if they are not topically related to them ( authority effect ) • The boost factor is able to capture sudden variations of citation rates and to spot potential breakthrough early on • Peaks in the evolution of the boost factor are not due to the landmark papers themselves but to the citation cascade towards earlier articles • The boost factor is more effective than traditional scientific metrics

¡ ¡ ¡ Acknowledgements Filippo Radicchi Dirk Helbing Claudio Castellano Raj Kumar Pan Sergi Lozano Young-Ho Eom Amin Mazloumian

C. Castellano, S. F., V. Loreto, Rev. Mod. Phys. 81, 591 (2009)