科學計量學(Scientometrics)利用數學、統計與資料分析方法與技術，蒐集、處理、解釋與預測學術傳播、成效、發展與動態等科技的特徵，對科技進行量化研究。就實務的技術而言，科學計量學利用書目計量的概念測量文本與資訊，並且利用科學地圖(science map)展現結果 (Börner 2010; Börner et al. 2003)。本研究利用網絡分析技術，從巨觀(國家)、中觀(機構)與微觀(作者)三種層次，探討Scientometrics期刊1978-2010年發表的2541筆論文上的合作情形。
過去對於Scientometrics有以下的相關研究，Schoepflin and Glänzel (2001) 利用1980、1989和1997三年出版的Scientometrics論文，發現科學政策(science policy)與科學社會學(the sociology of science)等主題相關的論文比率減少。Peritz and Bar-Ilan (2002) 以1990和2000年的Scientometrics論文，確認Research Policy和Social Studies of Science分別是第三和第四最常引用的期刊。Hou, Kretschmer, and Liu (2008)從Scientometrics2002到2004年論文上的作者合作網絡上發現一半以上的作者有合作的經驗，但是網絡的連結並不強而且疏鬆。Dutt, Garg, and Bali (2003)使用大量論文資料進行，研究資料期間為1978到2001，發現機構的平均論文數偏低，顯示研究的產出相當分散，而且以單一作者的論文為主，雖然多位作者的論文正蓄勢待發。
研究結果發現：
(1) 論文生產力較大的國家有美國、比利時、英國、荷蘭和西班牙。
(2) 機構與作者數隨時間增加，但是機構的平均論文數成長緩慢，近年的作者平均論文數則減少。
(3) 具有高中心性及中介性的一些機構可視為是合作網絡上的守門人(gatekeepers)。
(4) 近期較高生產力的作者取代了早期的重要作者。
Scientometrics的論文、作者和機構平均每年增加率為20%，顯示這個領域吸引愈來愈多的研究人員和機構加入。另外，Bettencourt et al. (2009) 以下面的公式指出當領域成長時，它的合作網路將會變得更為稠密。
而本研究三種層次的合作網絡，國家合作網絡的α值為 2.9533，機構與作者則分別為1.5222和1.2353。明顯的可以看出國家合作網絡相當快速地變得稠密，但由於單一作者論文的增加以及許多合作仍然是同一國家內的機構或同一機構內的作者彼此間的合作，使得機構合作網絡和作者合作網絡的α值較小。
在網絡的直徑(diameter)，也就是網絡上最長的路徑方面，國家合作網絡的直徑在1989到1998年是增長的情形，但在近十年則是減短；反之，機構合作網絡和作者合作網絡到2010年仍在持續增長。
測量三種層次合作網絡的節點的連結程度(connection degree)，其分布情形都符合冪次法則(power law)。節點的重要性可以從它們的程度中心性和中介中心性來推測，早期和近期的重要作者有很大的不同，在國家與機構方面的差別相當小。
比較三種層次的結果可以發現，較低層的結果會影響到上面的層次。例如有些作者的高排名不僅影響機構的排名，同時也會主導國家的排名；當具有高生產力的作者移動後，會牽動機構網絡的結構性變化。
Specifically, we would like to understand if and how collaborations at the author (micro) level impact collaboration patterns among institutions (meso) and countries (macro).
All 2,541 papers (articles, proceedings papers, and reviews) published in the international journal Scientometrics from 1978–2010 are analyzed and visualized across the different levels and the evolving collaboration networks are animated over time.
(1) USA, Belgium, and England dominated the publications in Scientometrics throughout the 33-year period, while the Netherlands and Spain were the subdominant countries;
(2) the number of institutions and authors increased over time, yet the average number of papers per institution grew slowly and the average number of papers per author decreased in recent years;
(3) a few key institutions, including Univ Sussex, KHBO, Katholieke Univ Leuven, Hungarian Acad Sci, and Leiden Univ, have a high centrality and betweenness, acting as gatekeepers in the collaboration network;
(4) early key authors (Lancaster FW, Braun T, Courtial JP, Narin F, or VanRaan AFJ) have been replaced by current prolific authors (such as Rousseau R or Moed HF).
Comparing results across the three levels reveals that results from one level might propagate to the next level, e.g., top rankings of a few key single authors can not only have a major impact on the ranking of their institution but also lead to a dominance of their country at the country level; movement of prolific authors among institutions can lead to major structural changes in the institution networks.
Scientometrics is a distinct discipline that performs quantitative studies of science and technology using mathematical, statistical, and data-analytical methods and techniques for gathering, handling, interpreting, and predicting a variety of features of the science and technology enterprise, including scholarly communication, performance, development, and dynamics.
The study presented here uses papers that appeared in Scientometrics, the flagship journal of the field (Chen et al. 2002) publishing a major percentage of works in scientometrics as well as in the field of informetrics (Bar-Ilan 2008) over the last 33 years.
For example, Schoepflin and Glänzel (2001) used papers published in Scientometrics for the years 1980, 1989, and 1997 to identify a decrease in the percentages of both the articles related to the subjects of science policy and to the sociology of science.
Peritz and Bar-Ilan (2002) used papers published in Scientometrics for the years 1990 and 2000 and confirmed that Research Policy and Social Studies of Science are the third and fourth most frequently referenced journals in articles published in Scientometrics.
Hou et al. (2008) analyzed the structure of scientific collaboration networks in scientometrics at the micro level (individuals) by using bibliographic data of all papers published in Scientometrics from the years 2002–2004. They found that although half the authors had co-authored with each other, the network was not strongly connected and the collaborative network in the field of scientometrics was very loose.
Dutt et al. (2003) analyzed Scientometrics papers published during 1978–2001, examining the distribution of countries and themes and comparing institutions and coauthors to show that the research output is highly scattered, as indicated by the average number of papers per institution and dominated by single-authored papers; however, multi-authored papers are gaining momentum.
Chen et al. (2010) introduced a multiple-perspective co-citation analysis for characterizing and interpreting the structure and dynamics of co-citation clusters of the field of information science between 1996 and 2008. He showed that the multiple-perspective method increases the interpretability and accountability of both author-citation analysis (ACA) and document- citation analysis (DCA) networks.
Wagner and Leydesdorff (2005) applied network analysis to map the growth of international co-authorships, and they found that international co-authorships can be explained based on the organizing principle of preferential attachment, although the attachment mechanism deviates from an ideal power-law.
Samoylenko et al. (2006) visualized the scientific world and its evolution by constructing minimum spanning trees (MSTs) and a two-dimensional map of scientific journals using the Science Citation Index from the Web of Science database for 1994–2001 and showed a linear structure of the scientific world with three major domains: physical sciences, life sciences, and medical sciences.
Perc (2010) studied the evolution of Slovenia’s scientist collaboration network from 1960 to 2010 with a yearly resolution and showed the network had a ‘‘small world’’ pattern and its growth was governed by near-linear preferential attachment. This paper will advance the existing works by studying the evolution of scientometrics at three different network levels.
Figure 1 shows the growth (annual and cumulative) of the number of papers, countries (or regions), institutions and authors from 1978 to 2010. By counting the annual numbers in each figure, we obtain average annual growth rates, which are 20.4 % (papers), 9.4 % (countries), 19.6 % (institutions), and 20.1 % (authors).
As Bettencourt et al. (2009) pointed out, when fields grow, their collaboration networks densify—i.e., the average number of edges per node increases over time. They found that the relation between the number of nodes and edges followed a simple scaling law with scaling exponent (α > 1):
Figure 2 shows that the scaling exponent a equals 2.9533 at the macro-country, 1.5222 at the meso-institution, and 1.2353 at the micro-author levels. It has the highest value for countries—i.e., the country collaboration networks densify rather quickly, which is also due to the fact that this is the network with the fewest nodes. However, a large number of within-country or within-institution collaborations or an increase in single-authored papers would also result in smaller α values.
The diameter of a collaboration network has major implications for information diffusion—the shorter a pathway of coauthor linkages that connects an author pair, the more likely knowledge diffuses.
Over the 33 years, the country collaboration network diameter grew from 1989 to 1998 (there were no edges before 1989), achieves the highest value in 1998, and decreases in the last 10 years. This might be due to the rather limited number of countries that perform scientometrics research.
The diameters of the institution and author collaboration networks increase continually and both reach a diameter d = 15 in 2010.
A closer look at the density of the three networks (the ratio of the number of actual edges to all possible edges in a fully connected graph with the same number of nodes) shows that both the meso and micro networks’ densities decrease over time while the macro network, which experienced a topological transition from large to decreasing diameter, shows an increase in density.
In an attempt to understand the structure of the 1978–2010 networks, the degree for each node in the network was determined and the node degree distribution p(k) plotted in Fig. 3. ... All three networks exhibit power law degree distributions.
To understand which countries, institutions, and authors play key roles in the three networks, the degree centrality (the number of links a node has) and betweenness centrality (nodes that have a high probability to occur on a randomly chosen shortest path between two randomly chosen nodes have a high betweenness) (Freeman 1977) values for each node were calculated. The resulting TOP-5 countries, TOP-10 institutions, and TOP-10 authors calculated for every 6 years (cumulatively from 1978) are listed in Tables 1 and 2.
In addition, the last table column shows the TOP-10 countries, institutions, and authors if only 2001–2010 data is considered. While the differences are minimal for countries and institutions, the list of TOP-10 authors changes considerably if only recent works are considered.
Figure 4 shows that, by the end of 2010, Belgium, USA, England, Germany, the Netherlands, China, and France are central network nodes with a large number of papers. These six countries not only link to each other but also to outside countries—e.g., Belgium and Germany have strong links to Hungary, and Belgium and England have strong links to Finland.
When analyzing the evolving institution collaboration networks, it becomes clear that a few key institutions manage to stay in the TOP-10 list—among them are the Univ Sussex, KHBO, Katholieke Univ Leuven, Hungarian Acad Sci, and Leiden Univ.
During the evolution of the co-author networks, early authors are replaced by current authors. Most TOP-10 authors from 1980 and 1986 are missing in the later years. Key authors listed in the TOP-10 lists around 1986 decline in ranking or are replaced by other authors.
One might assume that rankings on the author (micro) level impact the ranking of institution (meso) and country (macro) levels. While author rankings impact institution rankings; institution rankings are less predictive of country rankings, as exemplified below.
As can be seen in Table 3, USA ranks first in the number of institutions and the number of papers over the 33 year time span. However, the average number of papers per institution was low for the USA, especially when compared with Belgium, Netherlands, and Hungary. ... Similarly, while no single author in the USA appears in the TOP-10 lists, the number of all authors combined and the number of their papers results in a high country ranking.
Can one single author impact the ranking of an entire institution or country? The answer is yes. ... The 155 papers of the Hungarian Academy of Sciences were co-authored with 30 institutions, 22 of which were contributed by papers authored by Glänzel W. As for the 93 papers by the Katholieke Universiteit Leuven, 13 of 51 institution links were added by Glänzel W.
Over the 33 years, the number of countries grew steadily with a linear growth feature with USA, Belgium and England leading in terms of centrality and betweenness. ... As their share increases, they have a stronger impact on the evolution of scientometrics. Over time, more and more collaboration links are generated and the average node degree and network density increase as well (see Table 4).
It is important to point out that some top-ranking countries have a small number of top-ranking institutions (e.g., Katholieke Univ Leuven in Belgium) while other countries (USA) have a large number of contributing institutions.
Similarity, some top-ranking institutions have one or two top-ranking authors, e.g., Glänzel W and Rousseau R
That is, single authors can not only have a major impact on the ranking of their institution but also of their country.
At the same time, the growth rate of institutions, authors and papers for each year were similar about 20 %. It suggested that this field had been attracting more and more institutions and authors to join the field of scientometrics.
The co-author network analysis showed that many new authors joined the field of scientometrics, especially in the recent 8 years. The diameter, average degree, and density of the network show the same trends as those calculated for institutions.
While co-author networks experience the departure of senior and the arrival of young researchers, the institution and country networks seem to have a comparatively stable structure of key nodes.
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