Bibliometric statistical properties of the 100 largest European
  universities: prevalent scaling rules in the science system
Microsoft Word - Stat4ArXiv.doc
Bibliometric statistical properties of the 100 largest European 
universities: prevalent scaling rules in the science system  
Anthony F. J. van Raan 
Centre for Science and Technology Studies 
Leiden University 
Wassenaarseweg 52 
P.O. Box 9555 
2300 RB Leiden, the Netherlands 
Abstract 
For the 100 largest European universities we studied the statistical properties of 
bibliometric indicators related to research performance, field citation density and journal 
impact. We find a size-dependent cumulative advantage for the impact of universities in 
terms of total number of citations. In previous work a similar scaling rule was found at 
the level of research groups. Therefore we conjecture that this scaling rule is a prevalent 
property of the science system. We observe that lower performance universities have a 
larger size-dependent cumulative advantage for receiving citations than top-performance 
universities. We also find that for the lower-performance universities the fraction of not-
cited publications decreases considerably with size. Generally, the higher the average 
journal impact of the publications of a university, the lower the number of not-cited 
publications. We find that the average research performance does not ‘dilute’ with size. 
Evidently large universities, particularly top-performance universities are characterized 
by ‘big and beautiful’. They succeed in keeping a high performance over a broad range of 
activities. This most probably is an indication of their overall scientific and intellectual 
attractive power. Next we find that particularly for the lower-performance universities the 
field citation density provides a strong cumulative advantage in citations per publication. 
The relation between number of citations and field citation density found in this study can 
be considered as a second basic scaling rule of the science system. Top-performance 
universities publish in journals with significantly higher journal impact as compared to 
the lower performance universities. We find a significant decrease of the fraction of self-
citations with increasing research performance, average field citation density, and 
average journal impact. 
1. Introduction  
In previous articles (van Raan 2006a, 2006b, 2007) we presented an empirical approach 
to the study of the statistical properties of bibliometric indicators of research groups. Now 
we focus on a two orders of magnitude larger aggregation level within the science 
system: the university. Our target group consists of the 100 largest European 
universities. We will distinguish between different ‘dimensions’: top- and lower-
performance universities, higher and lower field citation densities, and higher and lower 
journal impact. In particular, we are interested in the phenomenon of size-dependent 
(size of a university in terms of number of publications) cumulative advantage1 of impact 
                                                 
1 By ‘cumulative advantage’ we mean that the dependent variable (for instance, number of citations of a 
university, C) increases in a disproportional, nonlinear (in this case: power law) way as a function of the 
independent variable (for instance, in the present study the size of a research university, in terms of number of 
publications, P). Thus, larger universities (in terms of P) do not just receive more citations (as can be 
expected), but they do so increasingly more advantageously: universities that are twice as large as other 
universities receive, on average, about 2.5 more citations.  
(in terms of numbers of citations), for different levels of research performance, field 
citation density and journal impact.   
Katz (1999) discussed scaling relationships between number of citations and number of 
publications across research fields and countries. He concluded that the science system is 
characterized by cumulative advantage, more particularly a size-dependent ‘Matthew 
effect’ (Merton 1968, 1988). As explained in footnote 1, this implies a nonlinear increase 
of impact with increasing size, demonstrated by the finding that the number of citations 
as a function of number of publications (in Katz’ study for 152 fields of science) exhibits a 
power law dependence with an exponent larger than 1. In our previous articles (van 
Raan 2006a, 2006b, 2007) we demonstrated a size-dependent cumulative advantage of 
the correlation between number of citations and number of publications also at the level 
of research groups. In this study we extent our observations to the level of entire 
universities.  
We focus on performance-related differences of bibliometric properties of universities. 
Particularly important are the citation characteristics of the research fields in which a 
university is active (the field citation densities) and the impact level of the journals used 
by a university. Seglen (1992, 1994) found a poor correlation between the impact of 
publications and journal impact at the level of individual publications. However, grouping 
publications in classes of journal impact yielded a high correlation between publication 
and journal impact. This grouping is determined by journal impact classes, and not by a 
‘natural’ grouping such as research groups and universities. In our previous study we 
showed a significant correlation between the average number of citations per publication 
of research groups, and the average journal impact of these groups. In this study we 
investigate whether this finding also holds at the level of entire universities.   
The structure of this study is as follows. Within a set of the 100 largest universities in 
Europe we distinguish in our analysis between performance, field citation densities and 
journal impact. In Section 2 we discuss the data material of the universities, the 
application of the method, and the calculation of the indicators. In Section 3 we analyse 
the data of the 100 largest European universities in the framework of size-dependent 
cumulative advantage and classify the results of the analysis in main observations. Our 
analysis of performance- and field density-related differences of bibliometric properties of 
universities reveals further interesting results, particularly on the role of journal impact. 
These observations are discussed in the last part of Section 3. Finally, in Section 4 we 
summarize the main outcomes of this study.  
2. Basic data and indicators derived from these data 
We studied the statistics of bibliometric indicators on the basis of all publications (as far 
as published in journals covered by the Citation Index, ‘CI publications’2) of the 100 
largest European universities for the period 1997-20043. This material is quite unique. To 
our knowledge no such compilations of very accurately collected publication sets on a 
large scale are used for statistical analysis of the characteristics of indicators at the 
university level. Obtaining data at the university level is not a trivial matter. The 
delineation of universities through externally available data such as the address 
information in the CI database is very problematic. For a thorough discussion of this 
problem, see Van Raan (2005a). The (CI-) publications were collected as part of a large 
                                                 
2 Thomson Scientific, the former Institute for Scientific Information (ISI) in Philadelphia, is the producer and 
publisher of the Citation Index system covered by the Web of Science. Throughout this article we use the 
acronym CI (Citation Index) to refer to this data system.  
3 We included Israel. We have left out Lomonosov University of Moscow. As far as number of publications 
concerns, this university is one of the largest in Europe (about 24,000 publications in the covered 8-year 
period) but the impact is so low (CPP/FCSm about 0.3) that it would have a very outlying position in the 
ranking. 
EC study on the scientific strengths of the European Union and its member states4. For a 
detailed discussion of methodological and technical issues we refer to Moed (2006). From 
a listing of more than 250 European universities we selected the 100 largest. The period 
covered is 1997-2004 for both publications and citations received by these publications. 
In total, the analysis involves the work of many thousands of senior researchers in 100 
large universities and covers around 1,5 million publications and 11 million citations 
(excluding self-citations), about 15% of the worldwide scientific output and impact. 
The indicators are calculated on the basis of a total time-period analysis. This means that 
publications are counted for the entire period (1997-2004) and citations are counted up 
to and including 2004 (e.g., for publications from 1997, citations are counted in the 
period 1997-2004, and for publications from 2004, citations are counted only in 2004). 
We are currently updating our data system with the 2005 and 2006 publication and 
citation data. 
We apply the CWTS5 standard bibliometric indicators. Only ‘external’ citations, i.e., 
citations corrected for self-citations, are taken into account. An overview of these 
indicators is given in the text box here below. For a detailed discussion we refer to Van 
Raan (1996, 2004, 2005b).  
Standard Bibliometric Indicators: 
• Number of publications P in CI-covered journals of a university in the specified period; 
• Number of citations C received by P during the specified period, without self-citations; including self-
citations: Ci, i.e., number of self-citations Sc = Ci – C, relative amount of self-citations Sc/Ci;  
• Average number of citations per publication, without self-citations (CPP); 
• Percentage of publications not cited (in the specified period) Pnc; 
• Journal-based worldwide average impact as an international reference level for a university (JCS, journal 
citation score, which is our journal impact indicator), without self-citations (on this world-wide scale!); in 
the case of more than one journal we use the average JCSm; for the calculation of JCSm the same 
publication and citation counting procedure, time windows, and article types are used as in the case of 
CPP; 
• Field-based6 worldwide average impact as an international reference level for a university (FCS, field 
citation score), without self-citations (on this world-wide scale!); in the case of more than one field (as 
almost always) we use the average FCSm; for the calculation of FCSm the same publication and citation 
counting procedure, time windows, and article types are used as in the case of CPP; we refer in this article 
to the FCSm indicator as the ‘field citation density’; 
• Comparison of the CPP of a university with the world-wide average based on JCSm as a standard, without 
self-citations, indicator CPP/JCSm; 
• Comparison of the CPP of a university with the world-wide average based on FCSm as a standard, without 
self-citations, indicator CPP/FCSm; 
• Ratio JCSm/FCSm is the relative, field-normalized journal impact indicator.  
In Table 1 we show as an example the results of our bibliometric analysis for the first 30 
universities within the European 100 largest. This table makes clear that our indicator 
calculations allow an extensive statistical analysis of these indicators for our set of 
universities. Of the above indicators, we regard the internationally standardized (field-
normalized) impact indicator CPP/FCSm as our ‘crown’ indicator. This indicator enables 
us to observe immediately whether the performance of a university is significantly far 
below (indicator value < 0.5), below (0.5 - 0.8), around (0.8 - 1.2), above (1.2 – 1.5), or 
far above (>1.5) the international (Western world dominated) impact standard averaged 
over all fields (van Raan 2004). 
                                                 
4 The ASSIST (Analysis and Studies of Statistics and Indicators on Science and Technology) project. 
5 Centre for Science and Technology Studies, Leiden University. 
6 We here use the definition of fields based on a classification of scientific journals into categories developed by 
Thomson Scientific/ISI. Although this classification is not perfect, it provides a clear and ‘fixed’ consistent field 
definition suitable for automated procedures within our data-system. 
Table 1: Largest 30 European universities 
 University P  C  CPP  Pnc  CPP/
1  UNIV CAMBRIDGE UK 36.349 361.681 9,95 29,1 1,63
2  UNIV COLL LONDON UK 34.407 346.028 10,06 26,9 1,46
3  UNIV OXFORD UK 33.780 355.856 10,53 29,5 1,67
4  IMPERIAL COLL LONDON UK 27.017 222.713 8,24 30,7 1,45
5  LUDWIG MAXIMILIANS UNIV MUNCHEN DE 23.519 177.317 7,54 30,8 1,14
6  UNIV PARIS VI PIERRE & MARIE CURIE FR 23.468 146.483 6,24 32,8 1,09
7  UNIV MILANO IT 23.006 175.181 7,61 30,0 1,11
8  UNIV UTRECHT NL 22.668 189.671 8,37 28,3 1,37
9  KATHOLIEKE UNIV LEUVEN BE 22.521 153.851 6,83 34,9 1,22
10  UNIV MANCHESTER  UK 22.470 137.812 6,13 34,4 1,16
11  UNIV WIEN AT 21.940 137.251 6,26 32,9 1,01
12  UNIV ROMA SAPIENZA IT 21.778 119.076 5,47 37,7 0,95
13  TEL AVIV UNIV IL 21.447 112.337 5,24 35,9 0,94
14  UNIV HELSINKI FI 21.034 179.662 8,54 28,5 1,38
15  LUNDS UNIV SE 20.631 157.944 7,66 27,9 1,21
16  KAROLINSKA INST STOCKHOLM SE 20.525 213.629 10,41 23,2 1,30
17  KOBENHAVNS UNIV DK 19.555 153.583 7,85 27,4 1,18
18  UNIV AMSTERDAM NL 19.333 163.417 8,45 28,9 1,35
19  UPPSALA UNIV SE 18.998 140.518 7,40 28,6 1,17
20  RUPRECHT KARLS UNIV HEIDELBERG DE 18.735 155.451 8,30 30,1 1,22
21  ETH ZURICH CH 18.611 148.078 7,96 29,8 1,52
22  KINGS COLL UNIV LONDON UK 18.601 161.460 8,68 28,7 1,32
23  HEBREW UNIV JERUSALEM IL 18.389 127.263 6,92 33,2 1,16
24  UNIV PARIS XI SUD FR 18.183 115.157 6,33 32,8 1,13
25  UNIV EDINBURGH UK 17.786 164.380 9,24 29,7 1,48
26  HUMBOLDT UNIV BERLIN DE 17.780 127.381 7,16 31,6 1,13
27  LEIDEN UNIV NL 16.832 147.821 8,78 26,9 1,26
28  UNIV ZURICH CH 16.783 154.154 9,19 29,2 1,33
29  UNIV BARCELONA ES 16.783 103.628 6,17 32,4 1,03
30  UNIV BRISTOL UK 16.387 119.960 7,32 29,7 1,31   
3. Results and Discussion 
3.1 Impact scaling and research performance  
In our previous study (van Raan 2006a, 2006b, 2007) we showed how a set of research 
groups is characterized in terms of the correlation between size (the total number of 
publications P of a specific research group7) and the total number of citations C received 
by a group. Now we calculated the same correlation for all 100 largest European 
universities. Fig. 3.1.1 shows that this correlation is described with a strong significance 
(coefficient of determination of the fitted regression is R2 = 0.79) by a power law: 
C(P) = 0.36 P 1.31 .  
At the lower side of P (and C) we observe a few ‘outliers’. These are universities with a 
considerably lower number of citations as compared to the other larger universities 
(among them Charles University of Prague and the University of Athens). We observe 
that the size of universities leads to a cumulative advantage (with exponent α=+1.31) 
for the number of citations received by these universities. Thus, the Matthew effect also 
works in at the aggregation level of entire universities. The intriguing question is how the 
                                                 
7 The number of publications is a measure of size in the statistical context described in this article. It is, 
however, a proxy for the real size of a research group or a university, for instance in terms number of staff full 
time equivalents (fte) available for research.  
research performance of the universities (measured by the indicator CPP/FCSm) relates 
to size-dependency. Gradual differentiation between top- and lower-performance 
(top/bottom 10%, 25%, and 50% of the CPP/FCSm distribution) enables us to study 
the correlation of C with P and possible scale effects (size-dependent cumulative 
advantage) in more detail. The results are presented in Figs. 3.1.2 - 3.1.4 and a 
summary of the findings in Table 3. 
 Correlation of C (per university) with P (per university) 
for the 100 largest European universities
y = 0.3566x1.308
R2 = 0.7929
10,000
100,000
1,000,000
1,000 10,000 100,000
Fig. 3.1.1: Correlation of the number of citations (C) received per university with the 
number of publications (P) of these universities for all 100 largest European universities. 
The group of highest performance universities (top-10%) does not have a cumulative 
advantage (i.e., exponent significantly8 > 1). The bottom-10% exponent is heavily 
determined by the outliers. The broader top-25% shows a slight (α=+1.16) and the 
bottom-25% a stronger cumulative advantage (α=+1.33). If we divide the entire set of 
universities in a top- and bottom-50% we see that both subsets have more or less equal 
exponents. Thus, the most intriguing finding is that the lowest performance universities 
have a larger size-dependent cumulative advantage than top-performance universities. 
This phenomenon was already observed at the level of research groups (van Raan 
2006a, 2006b, 2007). It is fascinating that within the science system this scaling rule 
covers at least two orders of magnitude in size of entities. Furthermore, the top-
performance universities are generally the larger ones, i.e., in the right hand side of the 
correlation function. 
                                                 
8 To estimate the influence of these noisy data, we randomly removed five universities. We found that the error 
in the exponent α is about ± 0.05. Thus, the noisiness of data remains within acceptable limits and does not 
substantially affect our findings.  
top-10% and bottom-10% of CPP/FCSm
y = 18.455x0.9355
R2 = 0.9556
y = 0.0833x1.4287
R2 = 0.6539
10,000
100,000
1,000,000
1,000 10,000 100,000
Fig. 3.1.2: Correlation of the number of citations (C) received per university with the 
number of publications (P) for the top-10% (of CPP/FCSm) universities (diamonds) and 
the bottom-10% universities (squares) within the 100 largest European universities. 
top-25% and bottom-25% of CPP/FCSm
y = 1.7776x1.1608
R2 = 0.8436
y = 0.2328x1.3293
R2 = 0.8291
10,000
100,000
1,000,000
1,000 10,000 100,000P
Fig. 3.1.3: Correlation of the number of citations (C) received per university with the 
number of publications (P) for the top-25% (of CPP/FCSm) universities (diamonds) and 
the bottom-25% universities (squares) within the 100 largest European universities. 
top-50% and bottom-50% of CPP/FCSm
y = 1.4839x1.171
R2 = 0.8197
y = 1.2745x1.1626
R2 = 0.7202
10,000
100,000
1,000,000
1,000 10,000 100,000
Fig. 3.1.4: Correlation of the number of citations (C) received per university with the 
number of publications (P) for the top-50% (of CPP/FCSm) universities (diamonds) and 
the bottom-50% universities (squares) with the 100 largest European universities. 
Table 3.1: Power law exponent α of the correlation of C with P for the 100 largest 
European universities in the indicated modalities. The differences in α between top and 
bottom modalities are indicated by ∆α(b,t). 
All 100 1.31 
top 10% 0.94 
bottom 10% 1.43 
∆α(b,t) 0.49 
top 25% 1.16 
bottom 25% 1.33 
∆α(b,t) 0.17 
top 50% 1.17 
bottom 50% 1.16 
∆α(b,t) -0.01 
An important feature of research impact is the number of not-cited publications. We 
analysed the correlation of the fraction (percentage) of not-cited-publications Pnc of the 
100 largest European universities with size (P) of a university. The results are shown in 
Fig. 3.1.5. We observe that the fraction of not-cited publications decreases with low 
significance as a function of size. The significance of the correlation is too low for clear 
results. Thus, as a further step we investigate this correlation with a distinction between 
top- and lower-performance universities. Fig. 3.1.6 shows the results for the top- and 
bottom-25%, and Fig. 3.1.7 for the top-50% and bottom-50% of the CPP/FCSm 
distribution of the 100 largest universities.   
 Correlation of Pnc (per university) with P (total per university) 
y = 126.14x-0.1425
R2 = 0.1239
100.0
1,000 10,000 100,000P
Fig. 3.1.5: Correlation of the percentage of not cited publications (Pnc) with the number 
of publications (P) for the entire set of the 100 largest European universities.  
top-25% and bottom-25% of CPP/FCSm
y = 58.445x-0.0705
R2 = 0.0535
y = 196.33x-0.1773
R2 = 0.2131
100.0
1,000 10,000 100,000
Fig. 3.1.6: Correlation of the relative number of not cited publications (Pnc) with the 
number of publications (P) for the top-25% (of CPP/FCSm) universities (diamonds), 
and the bottom-25% universities (squares).  
top-50% and bottom-50% of CPP/FCSm
y = 56.73x-0.0649
R2 = 0.0342
y = 80.722x-0.0902
R2 = 0.0466
100.0
1,000 10,000 100,000P
Fig. 3.1.7: Correlation of the relative number of not cited publications (Pnc) with the 
number of publications (P) for the top-50% (of CPP/FCSm) universities (diamonds), 
and for the bottom-50% universities (squares).  
The observations suggest that the fraction of non-cited publications decreases with size, 
particularly for the lower performance universities. This phenomenon was also found at 
the level of research groups (van Raan 2006a, 2006b, 2007) which means that we 
discovered another scaling rule in the science system covering at least two orders of 
magnitude. We notice, however, that this scaling rule for non-cited publications is less 
strong at the level of entire universities as compared to groups. Advantage by size works 
by a mechanism in which the number of not-cited publications is diminished. This 
mechanism works at the level of research groups as follows. The larger the number of 
publications in a group, the more those publications are ‘promoted’ which otherwise 
would have remained uncited. Thus, size reinforces an internal promotion mechanism, 
namely initial citation of these ‘stay behind’ publications in other more cited publications 
of the group. Then authors in other groups are stimulated to take notice of these stay 
behind publications and eventually decide to cite them. Consequently, the mechanism 
starts with within-group citation (which is not necessarily the same as self-citation), and 
subsequently spreads. It is obvious that particularly the lower performance groups will 
benefit from this mechanism. Top-performance groups do not ‘need’ the internal 
promotion mechanism to the same extent as low performance groups. This explains, at 
least in a qualitative sense, why top-performance groups show less, or even no 
cumulative advantage by size. Since an entire university is the sum of a large number of 
research groups, the above mechanism will also be visible at the university level.    
We also investigated the relation between research performance as measured by 
indicator CPP/FCSm with size in terms of P.  We find a very slight positive correlation as 
shown in Fig. 3.1.8 for all 100 universities and in Fig. 3.1.9 for the top- and bottom-25% 
of the CPP/FCSm distribution. This, however, this is certainly not a cumulative 
advantage; the exponent of the correlation is very small, around 0.2. Probably the most 
interesting aspect of this measurement is that performance does not decrease, not 
‘dilute’ with increasing size.   
 Correlation of CPP/FCSm (university) with P (total per university) 
y = 0.1117x0.2427
R2 = 0.2164
10.00
1,000 10,000 100,000
CPP/FCSm
Fig. 3.1.8: Correlation of CPP/FCSm with the number of publications (P) for the entire 
set of all 100 largest European universities. 
top-25% and bottom-25% of CPP/FCSm
y = 0.1285x0.209
R2 = 0.2101
y = 0.6862x0.0727
R2 = 0.1138
10.00
1,000 10,000 100,000
CPP/FCSm
Fig. 3.1.9: Correlation of CPP/FCSm with the number of publications (P) for the top-
25% (diamonds) and the bottom-25% (squares) of CPP/FCSm distribution of the 100 
largest European universities.  
3.2  Impact scaling, field citation density and journal impact 
In Fig. 3.2.1 we present the correlation of the number of citations with size for those 
universities among the 100 largest European universities that have high and low field 
citation densities, i.e., top-25% and bottom-25%, respectively, of the FCSm distribution. 
We observe that the high field density universities hardly have a cumulative advantage 
(exponent α = 1.09). The low field citation density universities have a considerably size-
dependent cumulative advantage (exponent α = 1.50).  
Correlation of C (total per university) with P (total per university) 
top-25% and bottom-25% of FCSm
y = 3.6829x1.0853
R2 = 0.8523
y = 0.0458x1.503
R2 = 0.8399
10,000
100,000
1,000,000
1,000 10,000 100,000
Figure 3.2.1: Correlation of the number of citations (C) with the number of publications 
(P) for the universities within the top- (diamonds) and the bottom-25% (squares) of the 
field citation density (FCSm) distribution. 
Correlation of C (total per university) with P (total per university) 
top-25% and bottom-25% of JCSm
y = 4.6851x1.0657
R2 = 0.9112
y = 0.0709x1.458
R2 = 0.7474
10,000
100,000
1,000,000
1,000 10,000 100,000
Figure 3.2.2: Correlation of the number of citations (C) with the number of publications 
(P) for the universities within the top- (diamonds) and the bottom-25% (squares) of the 
field citation density (JCSm) distribution. 
In Fig. 3.2.2 we present a similar correlation for the top- and bottom-25% of the JCSm, 
the average journal impact of a university. We see that these results are practically the 
same as in Fig. 3.2.1. Given the strong correlation of JCSm and FCSm at the level of 
universities, as illustrated in Fig. 3.2.3, this similarity can be expected. We remark, 
however, that the correlation of JCSm and FCSm has a power exponent 1.22 which 
means that the JCSm values increase in a nonlinear way (‘cumulatively’) with FCSm.  
 Correlation of JCSm (per university) with FCSm (per university) 
y = 0,7327x1,2191
R2 = 0,7033
Figure 3.2.3: Correlation of the average journal impact (JCSm) with the average field 
citation density (FCSm) for all 100 largest European universities.  
We now investigate the relation between citation impact of a university in terms of 
average number of citations per publication (CPP) on the one hand, and field citation 
density (FCSm) and journal impact (JCSm) on the other. Seglen (1994) showed that the 
citedness of individual publications CPP is not significantly affected by journal impact9. 
However, grouping publications in classes of journal impact yielded a high correlation 
between publication citedness and journal impact. We found that also a ‘natural’ grouping 
of publications, such as the work of a research group, leads to a high correlation of CPP 
and JCSm (van Raan 2006b, 2007).  
In this study we find that this is also the case at the aggregation level of entire 
universities. We find a significant correlation between the average number of citations 
per publication for the 100 largest European universities (CPP), and both the field 
citation density (FCSm) as well as the average journal impact of these universities 
(JCSm). We applied again the distinction between top- and lower-performance 
universities in order to find performance-related aspects in the above relation. The 
results are shown for the correlation of CPP with FCSm for the entire set of all 100 
largest European universities in Fig. 3.2.4, and for the top-performance (top-25% of 
CPP/FCSm) and lower performance (bottom-25% of CPP/FCSm) universities in Fig. 
3.2.5. The correlation of CPP with JCSm for the entire set of all 100 largest European 
universities is presented in Fig. 3.2.6 and for the top-performance and lower 
performance universities in Fig. 3.2.7. We see hat these correlations are very significant. 
                                                 
9 In Seglen’s work journal impact was defined with the ISI (Web of Science) journal impact factor; he did not 
consider the more sophisticated journal impact indicators such as the JCSm used in this study. 
 Correlation of CPP (per university) with FCSm (per university)
y = 0.5928x1.3654
R2 = 0.5357
10.00
100.00
Fig. 3.2.4: Correlation of CPP with FCSm for all 100 largest European universities. 
top-25% and bottom-25% of CPP/FCSm
y = 0.1712x1.9746
R2 = 0.7401
y = 1.3407x1.0219
R2 = 0.8316
10.00
100.00
Fig. 3.2.5: Correlation of CPP with FCSm for the top-25% (diamonds) and the bottom-
25% (squares) of CPP/FCSm distribution of the 100 largest European universities.  
 Correlation of CPP (per university) with JCSm (per university) 
y = 0.6942x1.2222
R2 = 0.907
10.00
100.00
Fig. 3.2.6: Correlation of CPP with JCSm for all 100 largest European universities. 
top-25% and bottom-25% of CPP/FCSm
y = 0.6384x1.238
R2 = 0.9224
y = 1.228x0.9641
R2 = 0.9497
10.00
100.00
Fig. 3.2.7: Correlation of CPP with JCSm for the top-25% (diamonds) and the bottom-
25% (squares) of CPP/FCSm distribution of the 100 largest European universities.  
Both the top- and lower-performance universities have more citations per publication 
(CPP) as a function of field citation density (FCSm, Fig.3.2.5) as well as of average 
journal impact (JCSm, Fig. 3.2.7). Clearly, the top universities generally have higher 
CPP values. We find that particularly for the lower-performance universities the field 
citation density (FCSm) provides a strong cumulative advantage in citations per 
publication (CPP) with exponent α = 1.97. The correlation of CPP with the average 
journal impact (JCSm) shows a less strong cumulative advantage for the lower-
performance universities, α = 1.24. We also observe clearly (Fig. 3.2.7) that most top-
performance universities publish in journals with significantly higher journal impact as 
compared to the lower performance universities.  Moreover, the top-25% universities 
perform in terms of citations per publications (CPP) with a factor of about 1.3 better than 
the bottom-25% universities in journals with the same average impact. An overview of 
the exponents of the correlation functions is given in Table 3.2. 
Table 3.2: Power law exponent α of the correlation of CPP with FCSm and with JCSm 
for the 100 largest European universities. The differences in α between top- and bottom-
modalities are given by ∆α(b,t).  
FCSm 
JCSm 
all 1.37 1.22 
top 25% 1.02 0.96 
bottom 25% 1.97 1.24 
∆α(b,t) 0.95 0.28 
Next to the impact measure CPP we also investigated the correlation of the field-
normalized research performance indicator (CPP/FCSm) of the 100 largest European 
universities with field citation density and with journal impact. The results are shown for 
the correlation of CPP/FCSm with FCSm for the entire set of all 100 largest European 
universities in Fig. 3.2.8, and for the top-performance (top-25% of CPP/FCSm) and 
lower performance universities in Fig. 3.2.9. The correlation of CPP/FCSm with JCSm 
for the entire set of all 100 largest European universities is presented in Fig. 3.2.10 and 
for the top-performance and lower performance universities in Fig. 3.2.11.  
 Correlation of CPP/FCSm with FCSm 
y = 0.5928x0.3654
R2 = 0.0763
10.00
1 10FCSm
CPP/FCSm
Fig. 3.2.8: Correlation of CPP/FCSm with FCSm for the entire set of the 100 largest 
European universities.  
top-25% and bottom-25% of CPP/FCSm
y = 0.1712x0.9746
R2 = 0.4095
y = 1.3407x0.0219
R2 = 0.0023
10.00
CPP/FCSm
Fig. 3.2.9: Correlation of CPP/FCSm with FCSm for the top-25% (diamonds) and the 
bottom-25% (squares) of CPP/FCSm distribution of the 100 largest European 
universities.  
 Correlation of CPP/FCSm with JCSm 
y = 0.3417x0.6452
R2 = 0.503
10.00
CPP/FCSm
Fig. 3.2.10: Correlation of CPP/FCSm with JCSm for the entire set of the 100 largest 
European universities.  
 top-25% and bottom-25% of CPP/FCSm
y = 0.2535x0.7627
R2 = 0.7952
y = 1.1046x0.116
R2 = 0.0815
10.00
CPP/FCSm
Fig. 3.2.11: Correlation of CPP/FCSm with JCSm for the top-25% (diamonds) and the 
bottom-25% (squares) of CPP/FCSm distribution of the 100 largest European 
universities.  
We observe that the research performance of the top universities is independent of field 
citation density (FCSm). For the lower-performance universities there is a slight increase 
of performance as a function of FCSm. The results for the average journal impact 
(JCSm) are similar but more outspoken. Again we notice that top-performance 
universities have a strong preference for the higher-impact journals.  
Finally, we analysed the correlation between the number of not-cited publications (Pnc) 
of a university and its average journal impact level (JCSm). The results are shown in Fig. 
3.2.12 for the entire set of 100 universities and in Fig. 3.2.13 for the top- en lower-
performance universities. We see a quite significant correlation between these two 
variables. Very clearly the top universities have the lowest Pnc. Given the strong 
correlation between CPP and JCSm (see Fig. 3.2.6) we can also expect a significant 
correlation between Pnc and CPP, as confirmed nicely by Fig. 3.2.14 for the entire set of 
100 universities and in Fig. 3.2.15 for the top- en lower-performance universities. Thus, 
we find that the higher the average journal impact of the publications of a university, the 
lower the number of not-cited publications. Also, the higher the average number of 
citation per publication in a university, the lower the number of not-cited publications. In 
other words, universities that are cited more per paper also have more cited papers. 
These findings underline the generally good correlation at the university level between 
the average number of citations per publication in a university, and its average journal 
impact.  
We also find that the relation between the relative number of not-cited publications 
(Pnc) and the mean number of citations per publication (CPP) can be written in good 
approximation as 
Pnc = 1/√(CPP). 
This expression reflects the characteristics of the citation-distribution function as it is the 
relation between the number of publications with zero citations and the average number 
of citations per publications. 
 Correlation of Pnc (per university) with JCSm per university) 
y = 105.22x-0.6333
R2 = 0.8054
100.0
Fig. 3.2.12: Correlation of the relative number of not cited publications (Pnc) with the 
mean journal impact (JCSm) of the 100 largest European universities. 
top-25% and bottom-25% of CPP/FCSm
y = 84.574x-0.5261
R2 = 0.8363
y = 111.24x-0.6516
R2 = 0.8182
100.0
Fig. 3.2.13: Correlation of the relative number of not cited publications (Pnc) with the 
mean journal impact (JCSm) for the top-25% (of CPP/FCSm) universities (diamonds), 
and the bottom-25% universities (squares).  
 Correlation of Pnc (per university) with CPP (per university) 
y = 85.039x-0.5058
R2 = 0.8459
100.0
1.00 10.00 100.00CPP
Fig. 3.2.14: Correlation of the relative number of not cited publications (Pnc) with the 
mean number of citations per publication (CPP) of the 100 largest European universities. 
top-25% and bottom-25% of CPP/FCSm
y = 86.762x-0.5053
R2 = 0.7551
y = 88.425x-0.5303
R2 = 0.9008
100.0
1.00 10.00 100.00
Fig. 3.2.15: Correlation of the relative number of not cited publications (Pnc) with the 
mean number of citations per publication (CPP) for the top-25% (of CPP/FCSm) 
universities (diamonds), and the bottom-25% universities (squares).  
3.3 Characteristics of self-citations 
In this section we present a first analysis of a specific feature of the science system, the 
statistical properties of self-citations. We calculated the correlation between size (the 
total number of publications P) and the total number of citations C for all 100 largest 
European universities. Fig. 3.3.1 shows that this correlation is described with high 
significance by a power law: 
Sc(P) = 0.53 P 1.15 .  
 Correlation of Sc (per university) with P (per university) 
y = 0.5289x1.148
R2 = 0.882
10000
100000
1,000 10,000 100,000P
Fig. 3.3.1: Correlation of the number of self-citations (Sc) received per university with 
the number of publications (P) of these universities, for all 100 largest European 
universities.  
At the lower side of P (and Sc) we again observe the ‘outliers’ as in the case of the 
(external) citations (Fig. 3.1.1). We find that the size of universities leads to a cumulative 
advantage (with exponent α=+1.15) for the number of self-citations given by these 
universities. Gradual differentiation between top- and lower-performance (top/bottom 
10%, 25%, and 50%) enables us to study the correlation of Sc with P in more detail as 
presented in Figs. 3.3.2 - 3.3.4. We see that the group of highest performance 
universities (top-10%) does not have a cumulative advantage (exponent around 1), 
whereas the bottom-10% exponent is heavily determined by the outliers. The broader 
top-25% and the bottom-25% show a slight cumulative advantage (α= 1.11 and 1.15, 
respectively). If we divide the entire set of universities in a top- and bottom-50% we see 
that both subsets have more or less equal exponents (around 1.11). 
In Fig. 3.3.5 we show that the fraction (percentage) of self-citations (%Sc) decreases 
slightly with size (P), but this correlation is not very significant. More significant is the 
decrease of the fraction of self-citations as a function of research performance 
CPP/FCSm, as shown in Fig. 3.3.6. We also observe a clear decrease of self-citations for 
the 100 largest universities in Europe as a function of average field citation density 
FCSm, Fig. 3.3.7, average journal impact JCSm, Fig. 3.3.8, and of field-normalized 
journal impact JCSm/FCSm, see Fig. 3.3.9. 
top-10% and bottom-10% of CPP/FCSm
y = 3.7993x0.9599
R2 = 0.9755
y = 0.0659x1.3587
R2 = 0.6437
10000
100000
1,000 10,000 100,000P
Fig. 3.3.2: Correlation of the number of self-citations (Sc) received per university with 
the number of publications (P), for the top-10% (of CPP/FCSm) universities 
(diamonds), and the bottom-10% universities (squares) with the 100 largest European 
universities. 
top-25% and bottom-25% of CPP/FCSm
y = 0.8272x1.1067
R2 = 0.8943
y = 0.4661x1.1531
R2 = 0.8385
10000
100000
1,000 10,000 100,000P
Fig. 3.3.3: Correlation of the number of self-citations (Sc) received per university with 
the number of publications (P), for the top-25% (of CPP/FCSm) universities 
(diamonds), and the bottom-25% universities (squares) with the 100 largest European 
universities. 
top-50% and bottom-50% of CPP/FCSm
y = 0.7546x1.1137
R2 = 0.8759
y = 0.7x1.1158
R2 = 0.8415
10000
100000
1,000 10,000 100,000P
Fig. 3.3.4: Correlation of the number of self-citations (Sc) received per university with 
the number of publications (P), for the top-50% (of CPP/FCSm) universities 
(diamonds), and the bottom-50% universities (squares) with the 100 largest European 
universities. 
 Correlation of %Sc (per university) with P (per university) 
y = 76.132x-0.1197
R2 = 0.1076
100.0
1,000 10,000 100,000P
Fig. 3.3.5: Correlation of the relative number of self-citations (%Sc) per university with 
the number of publications (P) of these universities, for all 100 largest European 
universities.  
 Correlation of %Sc with CPP/FCSm 
y = 25.98x-0.5349
R2 = 0.5853
100.0
0.10 1.00 10.00
CPP/FCSm
Fig. 3.3.6: Correlation of the relative number of self-citations (%Sc) per university with 
the performance (CPP/FCSm) of these universities, for all 100 largest European 
universities.  
Correlation of %Sc (per university) with FCSm 
y = 55.092x-0.4599
R2 = 0.2474
100.0
1 10FCSm
Fig. 3.3.7: Correlation of the relative number of self-citations (%Sc) per university with 
the field citation density (FCSm) of these universities, for all 100 largest European 
universities.  
Correlation of %Sc (per university) with JCSm 
y = 59.794x-0.4841
R2 = 0.5793
100.0
1 10JCSm
Fig. 3.3.8: Correlation of the relative number of self-citations (%Sc) per university with 
the average journal impact (JCSm) of these universities, for all 100 largest European 
universities.  
 Correlation of %Sc (per university) with JCSm/FCSm 
y = 25.94x-0.8393
R2 = 0.5499
100.0
0.10 1.00 10.00
JCSm/FCSm
Fig. 3.3.9: Correlation of the relative number of self-citations (%Sc) per university with 
the field-normalized journal impact (JCSm/FCSm) of these universities, for all 100 
largest European universities. 
4. Summary of the main findings and concluding remarks 
For the 100 largest European universities we studied statistical properties of bibliometric 
characteristics related to research performance, field citation density and journal impact. 
Our five main observations are as follows.  
First, we find a size-dependent cumulative advantage for the impact of universities in 
terms of total number of citations. Quite remarkably, lower performance universities 
have a larger size-dependent cumulative advantage for receiving citations than top-
performance universities. We found in previous work a similar scaling rule at the level of 
research groups and therefore we conjecture that this scaling rule is a prevalent property 
of the science system. We also observe that the top universities are about twice as 
efficient in receiving citations (C) as compared to the bottom-performance universities. 
Our criterion of top- or low performance is based on the field-normalized indicator 
CPP/FCSm. We hypothesize that in network terms this indicator represents the ‘fitness’ 
of a university as a node in the science system. It brings a university in a better position 
to acquire additional links (in terms of citations) on the basis of quality (high 
performance).  
Second, we find that for the lower-performance universities the fraction of not-cited 
publications decreases with size. We explain this phenomenon with a model in which size 
is advantageous in an ‘internal promotion mechanism’ to get more publications cited. 
Thus, in this model size is a distinctive parameter which acts as a bridge between the 
macro-picture (characteristics of the entire set of universities) and the micro-picture 
(characteristics within a university). We find that the higher the average journal impact 
of a university, the lower the number of not-cited publications. Also, the higher the 
average number of citations per publication in a university, the lower the number of not-
cited publications. In other words, universities that are cited more per paper also have 
more cited papers.  
Third, we find that the average research performance of university measured by our 
crown indicator CPP/FCSm does not ‘dilute’ with increasing size. Apparently large 
universities, particularly the top-performance universities are characterized by ‘big and 
beautiful’. In other words, they succeed in keeping a high performance over a broad 
range of activities. This most probably is an indication of their overall scientific and 
intellectual attractive power.  
Fourth, we observe that particularly the low field citation density and the low journal 
impact universities have a considerably size-dependent cumulative advantage for the 
total number of citations. We find that particularly for the lower-performance universities 
the field citation density (FCSm) provides a strong cumulative advantage in citations per 
publication (CPP). We also observe clearly that most top-performance universities 
publish in journals with significantly higher journal impact as compared to the lower 
performance universities.  Moreover, the top universities perform in terms of citations per 
publications (CPP) with a factor of about 1.3 better than the bottom universities in 
journals with the same average impact. The relation between number of citations and 
field citation density found in this study can be considered as a second basic scaling rule 
of the science system.  
Fifth, we find a significant decrease of the fraction of self-citations as a function of 
research performance CPP/FCSm, of the average field citation density FCSm, of the 
average journal impact JCSm, and of the field-normalized journal impact JCSm/FCSm.  
Acknowledgements 
The author would like to thank his CWTS colleagues Henk Moed and Clara Calero for the 
work to define and to delineate the universities, and for the data collection, data analysis 
and calculation of the bibliometric indicators.  
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