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  • 1. P. Chen (BU), S. Maslov (BNL), H. Xie (BNL) Impact and Productivity Measurements in a Changing Research Environment Washington, D.C., October 27, 2010 A Physicist’s Perspective on Citation Analysis
  • 2. P. Chen (BU), S. Maslov (BNL), H. Xie (BNL) Impact and Productivity Measurements in a Changing Research Environment Washington, D.C., October 27, 2010 A Physicist’s Perspective on Citation Analysis Observations about scientific citations: amusing facts/idle gossip evolution is governed by linear preferential attachment Summary & Outlook Google page rank analysis hidden “gems” h-index analysis danger of reliance on h predictive value of outliers
  • 3. Phys Rev Citation Data (as of July 07)
  • 4. Phys Rev Citation Data (as of July 07) 362,886 papers, 4,370,893 cites ￿# cites￿ = 12.04, ￿cite age￿= 7.82
  • 5. Phys Rev Citation Data (as of July 07) 362,886 papers, 4,370,893 cites ￿# cites￿ = 12.04, ￿cite age￿= 7.82 N.B.: Internal citations only; undercount by factor of 3-5. (for highly cited HEP papers; SPIRES)
  • 6. 32 papers with > 1000 citations Phys Rev Citation Data (as of July 07) 362,886 papers, 4,370,893 cites ￿# cites￿ = 12.04, ￿cite age￿= 7.82 N.B.: Internal citations only; undercount by factor of 3-5. (for highly cited HEP papers; SPIRES)
  • 7. 32 papers with > 1000 citations 158 papers with > 500 citations Phys Rev Citation Data (as of July 07) 362,886 papers, 4,370,893 cites ￿# cites￿ = 12.04, ￿cite age￿= 7.82 N.B.: Internal citations only; undercount by factor of 3-5. (for highly cited HEP papers; SPIRES)
  • 8. 32 papers with > 1000 citations 158 papers with > 500 citations 426 papers with > 300 citations Phys Rev Citation Data (as of July 07) 362,886 papers, 4,370,893 cites ￿# cites￿ = 12.04, ￿cite age￿= 7.82 N.B.: Internal citations only; undercount by factor of 3-5. (for highly cited HEP papers; SPIRES)
  • 9. 32 papers with > 1000 citations 158 papers with > 500 citations 426 papers with > 300 citations 3693 papers with > 100 citations Phys Rev Citation Data (as of July 07) 362,886 papers, 4,370,893 cites ￿# cites￿ = 12.04, ￿cite age￿= 7.82 N.B.: Internal citations only; undercount by factor of 3-5. (for highly cited HEP papers; SPIRES)
  • 10. 32 papers with > 1000 citations 158 papers with > 500 citations 426 papers with > 300 citations 3693 papers with > 100 citations 12519 papers with > 50 citations Phys Rev Citation Data (as of July 07) 362,886 papers, 4,370,893 cites ￿# cites￿ = 12.04, ￿cite age￿= 7.82 N.B.: Internal citations only; undercount by factor of 3-5. (for highly cited HEP papers; SPIRES)
  • 11. 32 papers with > 1000 citations 158 papers with > 500 citations 426 papers with > 300 citations 3693 papers with > 100 citations 12519 papers with > 50 citations 244281 papers with < 10 citations Phys Rev Citation Data (as of July 07) 362,886 papers, 4,370,893 cites ￿# cites￿ = 12.04, ￿cite age￿= 7.82 N.B.: Internal citations only; undercount by factor of 3-5. (for highly cited HEP papers; SPIRES)
  • 12. 32 papers with > 1000 citations 158 papers with > 500 citations 426 papers with > 300 citations 3693 papers with > 100 citations 12519 papers with > 50 citations 244281 papers with < 10 citations 51487 papers with 1 citation Phys Rev Citation Data (as of July 07) 362,886 papers, 4,370,893 cites ￿# cites￿ = 12.04, ￿cite age￿= 7.82 N.B.: Internal citations only; undercount by factor of 3-5. (for highly cited HEP papers; SPIRES)
  • 13. Phys Rev papers with >1000 cites (July 2003)
  • 14. Phys Rev papers with >1000 cites (July 2003) 1 PR 140 A1133 (1965) 3227 26.7 85972 Self Consistent Equations.. W. Kohn & L. J. Sham 2 PR 136 B864 (1965) 2460 28.7 70604 Inhomogeneous Electron Gas.. P. Hohenberg & W. Kohn cites age impactarticle title author(s)
  • 15. Phys Rev papers with >1000 cites (July 2003) 3 PRB 23 5048 (1981) 2079 14.4 29896 Self-Interaction Correction to.. J. P. Perdew & A. Zunger 1 PR 140 A1133 (1965) 3227 26.7 85972 Self Consistent Equations.. W. Kohn & L. J. Sham 2 PR 136 B864 (1965) 2460 28.7 70604 Inhomogeneous Electron Gas.. P. Hohenberg & W. Kohn cites age impactarticle title author(s)
  • 16. Phys Rev papers with >1000 cites (July 2003) 3 PRB 23 5048 (1981) 2079 14.4 29896 Self-Interaction Correction to.. J. P. Perdew & A. Zunger 4 PRL 45 566 (1980) 1781 15.4 27463 Ground State of the Electron.. D. M. Ceperley & B. J. Alder 1 PR 140 A1133 (1965) 3227 26.7 85972 Self Consistent Equations.. W. Kohn & L. J. Sham 2 PR 136 B864 (1965) 2460 28.7 70604 Inhomogeneous Electron Gas.. P. Hohenberg & W. Kohn cites age impactarticle title author(s)
  • 17. Phys Rev papers with >1000 cites (July 2003) 3 PRB 23 5048 (1981) 2079 14.4 29896 Self-Interaction Correction to.. J. P. Perdew & A. Zunger 4 PRL 45 566 (1980) 1781 15.4 27463 Ground State of the Electron.. D. M. Ceperley & B. J. Alder 5 PR 108 1175 (1957) 1364 20.2 27526 Theory of Superconductivity Bardeen, Cooper, Schrieffer 1 PR 140 A1133 (1965) 3227 26.7 85972 Self Consistent Equations.. W. Kohn & L. J. Sham 2 PR 136 B864 (1965) 2460 28.7 70604 Inhomogeneous Electron Gas.. P. Hohenberg & W. Kohn cites age impactarticle title author(s)
  • 18. Phys Rev papers with >1000 cites (July 2003) 3 PRB 23 5048 (1981) 2079 14.4 29896 Self-Interaction Correction to.. J. P. Perdew & A. Zunger 4 PRL 45 566 (1980) 1781 15.4 27463 Ground State of the Electron.. D. M. Ceperley & B. J. Alder 5 PR 108 1175 (1957) 1364 20.2 27526 Theory of Superconductivity Bardeen, Cooper, Schrieffer 6 PRL 19 1264 (1967) 1306 15.5 20191 A Model of Leptons S. Weinberg 1 PR 140 A1133 (1965) 3227 26.7 85972 Self Consistent Equations.. W. Kohn & L. J. Sham 2 PR 136 B864 (1965) 2460 28.7 70604 Inhomogeneous Electron Gas.. P. Hohenberg & W. Kohn cites age impactarticle title author(s)
  • 19. Phys Rev papers with >1000 cites (July 2003) 3 PRB 23 5048 (1981) 2079 14.4 29896 Self-Interaction Correction to.. J. P. Perdew & A. Zunger 4 PRL 45 566 (1980) 1781 15.4 27463 Ground State of the Electron.. D. M. Ceperley & B. J. Alder 5 PR 108 1175 (1957) 1364 20.2 27526 Theory of Superconductivity Bardeen, Cooper, Schrieffer 6 PRL 19 1264 (1967) 1306 15.5 20191 A Model of Leptons S. Weinberg 7 PRB 12 3060 (1975) 1259 18.4 23103 Linear Methods in Band Theory O. K. Andersen 8 PR 124 1866 (1961) 1178 28.0 32949 Effects of Configuration.. U. Fano 9 RMP 57 287 (1985) 1055 9.2 9674 Disordered Electronic Systems P. A. Lee & T. V. Ramakrishnan 10 RMP 54 437 (1982) 1045 10.8 11307 Electronic Properties of.. T. Ando, A. B. Fowler, & F. Stern 11 PRB 13 5188 (1976) 1023 20.8 21227 Special Points for Brillouin.. H. J. Monkhorst & J. D. Pack 1 PR 140 A1133 (1965) 3227 26.7 85972 Self Consistent Equations.. W. Kohn & L. J. Sham 2 PR 136 B864 (1965) 2460 28.7 70604 Inhomogeneous Electron Gas.. P. Hohenberg & W. Kohn cites age impactarticle title author(s)
  • 20. Phys Rev papers with >1000 cites (July 2003) 3 PRB 23 5048 (1981) 2079 14.4 29896 Self-Interaction Correction to.. J. P. Perdew & A. Zunger 4 PRL 45 566 (1980) 1781 15.4 27463 Ground State of the Electron.. D. M. Ceperley & B. J. Alder 5 PR 108 1175 (1957) 1364 20.2 27526 Theory of Superconductivity Bardeen, Cooper, Schrieffer 6 PRL 19 1264 (1967) 1306 15.5 20191 A Model of Leptons S. Weinberg 7 PRB 12 3060 (1975) 1259 18.4 23103 Linear Methods in Band Theory O. K. Andersen 8 PR 124 1866 (1961) 1178 28.0 32949 Effects of Configuration.. U. Fano 9 RMP 57 287 (1985) 1055 9.2 9674 Disordered Electronic Systems P. A. Lee & T. V. Ramakrishnan 10 RMP 54 437 (1982) 1045 10.8 11307 Electronic Properties of.. T. Ando, A. B. Fowler, & F. Stern 11 PRB 13 5188 (1976) 1023 20.8 21227 Special Points for Brillouin.. H. J. Monkhorst & J. D. Pack 1 PR 140 A1133 (1965) 3227 26.7 85972 Self Consistent Equations.. W. Kohn & L. J. Sham 2 PR 136 B864 (1965) 2460 28.7 70604 Inhomogeneous Electron Gas.. P. Hohenberg & W. Kohn cites age impactarticle title author(s) top 10 cited Phys Rev papers (July 2007)
  • 21. Phys Rev papers with >1000 cites (July 2003) 3 PRB 23 5048 (1981) 2079 14.4 29896 Self-Interaction Correction to.. J. P. Perdew & A. Zunger 4 PRL 45 566 (1980) 1781 15.4 27463 Ground State of the Electron.. D. M. Ceperley & B. J. Alder 5 PR 108 1175 (1957) 1364 20.2 27526 Theory of Superconductivity Bardeen, Cooper, Schrieffer 6 PRL 19 1264 (1967) 1306 15.5 20191 A Model of Leptons S. Weinberg 7 PRB 12 3060 (1975) 1259 18.4 23103 Linear Methods in Band Theory O. K. Andersen 8 PR 124 1866 (1961) 1178 28.0 32949 Effects of Configuration.. U. Fano 9 RMP 57 287 (1985) 1055 9.2 9674 Disordered Electronic Systems P. A. Lee & T. V. Ramakrishnan 10 RMP 54 437 (1982) 1045 10.8 11307 Electronic Properties of.. T. Ando, A. B. Fowler, & F. Stern 11 PRB 13 5188 (1976) 1023 20.8 21227 Special Points for Brillouin.. H. J. Monkhorst & J. D. Pack 1 PR 140 A1133 (1965) 3227 26.7 85972 Self Consistent Equations.. W. Kohn & L. J. Sham 2 PR 136 B864 (1965) 2460 28.7 70604 Inhomogeneous Electron Gas.. P. Hohenberg & W. Kohn cites age impactarticle title author(s) top 10 cited Phys Rev papers (July 2007) cites age impactarticle title author(s) 3 PRB 23 5048 (1981) 3007 Self-Interaction Correction to.. J. P. Perdew & A. Zunger 4 PRL 45 566 (1980) 2514 Ground State of the Electron.. D. M. Ceperley & B. J. Alder 1 PR 140 A1133 (1965) 4930 Self Consistent Equations.. W. Kohn & L. J. Sham 2 PR 136 B864 (1965) 3564 Inhomogeneous Electron Gas.. P. Hohenberg & W. Kohn
  • 22. Phys Rev papers with >1000 cites (July 2003) 3 PRB 23 5048 (1981) 2079 14.4 29896 Self-Interaction Correction to.. J. P. Perdew & A. Zunger 4 PRL 45 566 (1980) 1781 15.4 27463 Ground State of the Electron.. D. M. Ceperley & B. J. Alder 5 PR 108 1175 (1957) 1364 20.2 27526 Theory of Superconductivity Bardeen, Cooper, Schrieffer 6 PRL 19 1264 (1967) 1306 15.5 20191 A Model of Leptons S. Weinberg 7 PRB 12 3060 (1975) 1259 18.4 23103 Linear Methods in Band Theory O. K. Andersen 8 PR 124 1866 (1961) 1178 28.0 32949 Effects of Configuration.. U. Fano 9 RMP 57 287 (1985) 1055 9.2 9674 Disordered Electronic Systems P. A. Lee & T. V. Ramakrishnan 10 RMP 54 437 (1982) 1045 10.8 11307 Electronic Properties of.. T. Ando, A. B. Fowler, & F. Stern 11 PRB 13 5188 (1976) 1023 20.8 21227 Special Points for Brillouin.. H. J. Monkhorst & J. D. Pack 1 PR 140 A1133 (1965) 3227 26.7 85972 Self Consistent Equations.. W. Kohn & L. J. Sham 2 PR 136 B864 (1965) 2460 28.7 70604 Inhomogeneous Electron Gas.. P. Hohenberg & W. Kohn cites age impactarticle title author(s) top 10 cited Phys Rev papers (July 2007) cites age impactarticle title author(s) 3 PRB 23 5048 (1981) 3007 Self-Interaction Correction to.. J. P. Perdew & A. Zunger 4 PRL 45 566 (1980) 2514 Ground State of the Electron.. D. M. Ceperley & B. J. Alder 1 PR 140 A1133 (1965) 4930 Self Consistent Equations.. W. Kohn & L. J. Sham 2 PR 136 B864 (1965) 3564 Inhomogeneous Electron Gas.. P. Hohenberg & W. Kohn 6 PRB 13 5188 (1976) 2277 Special Points for Brillouin.. H. J. Monkhorst & J. D. Pack 5 PRL 77 3865 (1996) 2478 Generalized Gradient Approx... Perdew, Burke, Ernzerhof 7 PRB 54 11169 (1996) 1933 EfficientIterativeSchemes.... G. Kresse & J. Furthmuller 8 PRB 43 1993 (1991) 1776 EfficientPseudopotentialsfor.... N. Troullier & J.L. Martins 9 PRB 41 7892 (1990) 1749 SoftSelf-ConsistentPseudopotentials... D. Vanderbilt
  • 23. Phys Rev papers with >1000 cites (July 2003) 3 PRB 23 5048 (1981) 2079 14.4 29896 Self-Interaction Correction to.. J. P. Perdew & A. Zunger 4 PRL 45 566 (1980) 1781 15.4 27463 Ground State of the Electron.. D. M. Ceperley & B. J. Alder 5 PR 108 1175 (1957) 1364 20.2 27526 Theory of Superconductivity Bardeen, Cooper, Schrieffer 6 PRL 19 1264 (1967) 1306 15.5 20191 A Model of Leptons S. Weinberg 7 PRB 12 3060 (1975) 1259 18.4 23103 Linear Methods in Band Theory O. K. Andersen 8 PR 124 1866 (1961) 1178 28.0 32949 Effects of Configuration.. U. Fano 9 RMP 57 287 (1985) 1055 9.2 9674 Disordered Electronic Systems P. A. Lee & T. V. Ramakrishnan 10 RMP 54 437 (1982) 1045 10.8 11307 Electronic Properties of.. T. Ando, A. B. Fowler, & F. Stern 11 PRB 13 5188 (1976) 1023 20.8 21227 Special Points for Brillouin.. H. J. Monkhorst & J. D. Pack 1 PR 140 A1133 (1965) 3227 26.7 85972 Self Consistent Equations.. W. Kohn & L. J. Sham 2 PR 136 B864 (1965) 2460 28.7 70604 Inhomogeneous Electron Gas.. P. Hohenberg & W. Kohn cites age impactarticle title author(s) top 10 cited Phys Rev papers (July 2007) 10 PR 108 1175 (1957) 1650 Theory of Superconductivity Bardeen, Cooper, Schrieffer cites age impactarticle title author(s) 3 PRB 23 5048 (1981) 3007 Self-Interaction Correction to.. J. P. Perdew & A. Zunger 4 PRL 45 566 (1980) 2514 Ground State of the Electron.. D. M. Ceperley & B. J. Alder 1 PR 140 A1133 (1965) 4930 Self Consistent Equations.. W. Kohn & L. J. Sham 2 PR 136 B864 (1965) 3564 Inhomogeneous Electron Gas.. P. Hohenberg & W. Kohn 6 PRB 13 5188 (1976) 2277 Special Points for Brillouin.. H. J. Monkhorst & J. D. Pack 5 PRL 77 3865 (1996) 2478 Generalized Gradient Approx... Perdew, Burke, Ernzerhof 7 PRB 54 11169 (1996) 1933 EfficientIterativeSchemes.... G. Kresse & J. Furthmuller 8 PRB 43 1993 (1991) 1776 EfficientPseudopotentialsfor.... N. Troullier & J.L. Martins 9 PRB 41 7892 (1990) 1749 SoftSelf-ConsistentPseudopotentials... D. Vanderbilt
  • 24. Citation histories of 3 classic PR papers 1950 1970 1990 2010 0 50 100 150 200 KS EPR BCS av. citation age 59.6 (as of 7/03) #1, 4420 internal cites (as of 04/02/08) 1st PR paper > 1000 cites 5145 internal cites 17057 total cites (10/16/10)
  • 25. “Sleeping Beauties” # cites > 300 <cite age>/paper age > 3/4
  • 26. ⇒ colossal magnetoresistance 8 papers total, 5 on double exchange “Sleeping Beauties” # cites > 300 <cite age>/paper age > 3/4
  • 27. 1960 1980 2000 0 20 40 60 80 100 de Gennes Wollan & Koehler Goodenough Anderson & Hasegawa Zener ⇒ colossal magnetoresistance 8 papers total, 5 on double exchange “Sleeping Beauties” # cites > 300 <cite age>/paper age > 3/4
  • 28. 0 200 400 600 800 number of citations k 0 50 100 150 200 attachmentrateAk 0 50 100 150 0 25 50 1990-99 1980-99 1970-99 1893-1999 Physical Review Citation Data, 1893-2003 citation rate Ak What is the Citation Rate? Physics Today 58, 49 (2005)
  • 29. 0 200 400 600 800 number of citations k 0 50 100 150 200 attachmentrateAk 0 50 100 150 0 25 50 1990-99 1980-99 1970-99 1893-1999 Physical Review Citation Data, 1893-2003 citation rate Ak What is the Citation Rate? Physics Today 58, 49 (2005)
  • 30. → Ak ∝ k 0 200 400 600 800 number of citations k 0 50 100 150 200 attachmentrateAk 0 50 100 150 0 25 50 1990-99 1980-99 1970-99 1893-1999 Physical Review Citation Data, 1893-2003 citation rate Ak What is the Citation Rate? Physics Today 58, 49 (2005)
  • 31. 1 10 100 1000 k 10 −6 10 −5 10 −4 10 −3 10 −2 10 −1 C(k) Cumulative Citation Distribution C(k) = Ae−a ln k−b(ln k)2 a = 0.40, b = 0.16
  • 32. Google Page Rank for Citations Brin & Page (1999) Evolution equation for websurfers on a network: number of websurfers on node iGi =
  • 33. Google Page Rank for Citations Brin & Page (1999) Evolution equation for websurfers on a network: number of websurfers on node iGi = random walk propagation Gi = (1 − d) j nn i Gj kout j + d N i j Gj ￿ kout j manna from heaven
  • 34. Gi = (1 − d) j nn i Gj kout j + d N i j Gi ￿ kout j Google Page Rank for Citations Brin & Page (1999) Evolution equation for websurfers on a network: number of websurfers on node iGi = manna from heaven random walk propagation
  • 35. Brin/Page: d=0.15 (bored after 6 clicks) Gi = (1 − d) j nn i Gj kout j + d N i j Gi ￿ kout j Google Page Rank for Citations Brin & Page (1999) Evolution equation for websurfers on a network: number of websurfers on node iGi = manna from heaven random walk propagation
  • 36. Brin/Page: d=0.15 (bored after 6 clicks) Here: d=0.50 (don’t cite beyond 2 generations) Gi = (1 − d) j nn i Gj kout j + d N i j Gi ￿ kout j Google Page Rank for Citations Brin & Page (1999) Evolution equation for websurfers on a network: number of websurfers on node iGi = manna from heaven random walk propagation
  • 37. 10 0 10 1 10 2 10 3 10 4 number of citations 10 0 10 1 10 2 10 3 averagegooglenumber Google Number & Citation Counts slope 1 P. Chen, H. Xie, S. Maslov, and S. Redner, J. Informetrics 1, 8 (2007)
  • 38. 0 500 1000 1500 number of citations 0 100 200 300 400 500googlenumber
  • 39. Cabibbo 0 500 1000 1500 number of citations 0 100 200 300 400 500googlenumber
  • 40. Cabibbo BCS 0 500 1000 1500 number of citations 0 100 200 300 400 500googlenumber
  • 41. Cabibbo BCS K/S H/K 0 500 1000 1500 number of citations 0 100 200 300 400 500googlenumber
  • 42. Cabibbo BCS K/S H/K WeinbergOnsager 0 500 1000 1500 number of citations 0 100 200 300 400 500googlenumber
  • 43. Cabibbo BCS K/S H/K WeinbergOnsager Slater W/S Anderson G4 F/GM 0 500 1000 1500 number of citations 0 100 200 300 400 500googlenumber
  • 44. Cabibbo BCS K/S H/K WeinbergOnsager Slater W/S Anderson G4 F/GM 0 500 1000 1500 number of citations 0 100 200 300 400 500googlenumber S Hi Tc DLA GlauberW/S GM/B Fano
  • 45. The h-Index h definition: ≧ h publication with ≧ h citations
  • 46. The h-Index h definition: ≧ h publication with ≧ h citations 0 10000 20000 4h 2 0 10000 20000 c
  • 47. The h-Index h definition: ≧ h publication with ≧ h citations 0 10000 20000 4h 2 0 10000 20000 c result: h = ￿ c/4 J. Stat. Mech. L03005, (2010)
  • 48. r = √ c/2h 0.5 1 1.5 2 0 1 2 P(r) Distribution of √ c/2h
  • 49. r = √ c/2h 0.5 1 1.5 2 0 1 2 P(r) Distribution of √ c/2h •extraordinary publications •timely review articles •few but good publications •junior researchers who are the outliers?
  • 50. Summary & Outlook
  • 51. Summary & Outlook Citation analysis is fun! (but a Pandora’s box) Page rank analysis: helps uncover hidden “gems” Data motivate and test theories of growing citation networks h-index analysis: h is equivalent to √c but outliers, properly interpreted, are revealing Regularities and revealing irregularities
  • 52. Summary & Outlook Future: Deeper analysis of citation data: contextual information, specialization Larger data sources: test universality of citation statistics Citation analysis is fun! (but a Pandora’s box) Page rank analysis: helps uncover hidden “gems” Data motivate and test theories of growing citation networks h-index analysis: h is equivalent to √c but outliers, properly interpreted, are revealing Regularities and revealing irregularities