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

Source of data

Citation statistics

Papers are classified in 172 scientific disciplines

(from Acoustics to Zoology)‏

Dependence on field (ISI category)!

Could c0 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

Affiliation 1 Affiliation 2 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

1/3 1/3 1/3

Paper

¡ ¡ ¡Summary of statistics

−180 −150 −120 −90 −60 −30 30 60 90 120 150 180 −70 −50 −30 −10 10 30 50 70 100 101 102 103 104 105 106 Ncontribution

World publications: density- equalizing map

• M. Gastner, M. E. J. Newman, Proc. Natl. Acad. Sci. U.S.A. 101, 7499 (2004)

¡ ¡ ¡World citations: map

• M. Gastner, M. E. J. Newman, Proc. Natl. Acad. Sci. U.S.A. 101, 7499 (2004)

World citations: density- equalizing map

World citation averages

World citation distributions

100 102 104 NPub 10−10 10−8 10−6 10−4 10−2 100 P(NPub)

α ∼-1.41

100 102 104 106 NCite P(NCite)

α ∼-1.40

10−2 100 102 104 106 wCite

ij

P(wCite

ij

)

wij wii

sin

City-level citation distributions

City citation statistics: correlations

106 100 101 102 103 104 kin

j

100 102 104 106 sin

j

α ∼2.20 α ∼0.87

103 106 109 1012 sout

i

sin

j

10−4 10−2 100 102 104 wCite

ij

α ∼1.00 α ∼0.12

10−4 10−3 10−2 10−1 100

City-level collaborations: distributions and correlations

10−2 100 102 104 wCol

ij

10−6 10−4 10−2 100 Pc(wCol

ij )

wij wii 100 101 102 103 104 105 si 0.0 0.2 0.4 0.6 0.8 1.0 wCol

ii /si

100 102 104 ki 100 102 104 si

α ∼1.61

102 104 106 108 1010 sisj 10−4 10−2 100 102 104 wCol

ij

α ∼0.97 α ∼0.16

10−4 10−3 10−2 10−1 100

Citation vs collaborations

100 102 104 wcol

ij

10−2 100 102 104 106 wcite

ij

+ wcite

ji

α ∼1.06

10−2 100 102 104 wcol

ij

10−2 100 102 104

α ∼0.82

10−4 10−3 10−2 10−1 100

Gravity law

wij ∝ sout

i

sin

j

dα

ij

Gravity law: citations

Gravity law: collaborations

Gravity law: link probability vs distance

Cites vs number of authors (I)

5 10 15 20 NAuthors 100 101 102 103 104 hnci

Cites vs number of authors (II)

2 4 6 8 10 NCities 10−4 10−3 10−2 10−1 100 hnci

Cites vs number of authors (III)

2 4 6 8 10 NCountries hnci

Cites vs number of authors: summary

Funding vs citations

101 102 103 104 105 106 Npub

α ∼0.90 α ∼0.96

100 101 102 103 104 105 106 R&D expense (M $) 102 103 104 105 106 107 Ncite

α ∼0.99

101 102 103 104 105 106 Nresearcher

α ∼0.98

Funding vs citations

103 104 105 106 R&D expense /Nresearcher ($) 2 4 6 8 10 12 14 hnci

LV BE FR BG BA HR BN DE JP HU CH DZ MK BR ET FI UY DK RU MT NL PT RS UA PY TR LK TN NZ LU LS TH PK PH RO IS PL GT CO GR CN CL EE CA IR ZA EC IT CZ CY AR AU GB IN CR IE EG ES MD MG MA PA SG NO US LT SK KR SI KW SN SC MZ MY MX SE AT World average citation 120,000$

120,000 $

Funding vs citations

0.4 0.7 1.0 1.3 1.6 Bias

Total Citations

0.0 0.5 1.0 1.5 2.0 2.5 Bias

Top 1% cited papers

0.0 0.5 1.0 1.5 2.0 2.5 Bias

Top 10% cited papers

0.0 0.5 1.0 1.5 2.0 Bias

Top 100 Science Journals

United States China United Kingdom Japan Germany Canada France Italy India South Korea Spain Australia Russia Netherlands Taiwan Brazil Turkey Sweden Switzerland Poland Belgium Israel Iran Greece Denmark Finland Austria Mexico Singapore Norway Czech Republic Portugal South Africa New Zealand Argentina Ireland Hungary Egypt Romania Ukraine 0.0 0.5 1.0 1.5 2.0 Bias

Top 100 SocialScience Journals

bias for country i = N set

i

P

i N set i

× P

i Ni

Ni

¡ ¡ ¡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

• f cites of papers of a country stays below the

world average.

• Write papers with many people
• Get good neighbors
• Do international collaborations
• Get more funding!

How to get more citations?

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]

Rw(t) = R>t,w R<t,w

The boost factor

Year B

• s

t f a c t

• r

MR Capecchi JC Mather RY Tsien RB Myerson

a b c d

The boost factor vs standard indicators

Year t

E ff e c t s i z e

Normalized index value

MR Capecchi JC Mather RY Tsien RB Myerson

Boost factor

• Avg. Citations

per paper Cumulative citations h-index

a b c d

¡ ¡ ¡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

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

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