Jensen, P., & Lutkouskaya, K. (2014). The many dimensions of laboratories’ interdisciplinarity. Scientometrics, 98(1), 619-631.

Jensen, P., & Lutkouskaya, K. (2014). The many dimensions of laboratories’ interdisciplinarity. Scientometrics, 98(1), 619-631.

Scientometrics

本研究提出六種指標來測量研究機構的跨學科性。最廣義的來說，跨學科性可以視為不同學科某種程度的整合 (Weingart and Stehr 2000; Porter and Rafols 2009; Marcovich and Shinn 2011; Wagner et al. 2011; Rafols et al. 2012)，為了將這個想法轉換為量化的指標，本研究認為需要考慮三個問題：
1. 如何定義一個學科
2. 在什麼層次達到整合
3. 學科連結需要到達什麼程度

在學科的定義上，本研究提出三種方式：一、因為是分析CNRS的實驗室，自然可採用CNRS的學科組織(disciplinary organization)，包括10個研究所(institutes)以及進一步細分成的40個組(sections)；二、如同其他先前的研究，使用WoS(Web of Science)的224種期刊主題分類(Journal Subject Categories, JSCs)；三、將文件根據共同的參考文獻，以叢集演算法(clustering algorithms)由下往上地(bottom-up)歸類成認知叢集(cognitive clusters)。在整合的層次，則探討實驗室與論文兩個層級。

以實驗室的跨領域程度來說，較簡單的方式可以定義為：

此處的pi是實驗室的論文在期刊主題分類JSC i上的比例。

除了上述的定義之外，本研究還使用的Stirling’s (2007)方法來表現多樣性的三個不同面向：不同類別的數量(variety)、在各類別上的分布均勻程度(balance)、以及表現類別間的差異(disparity) (Porter and Rafols 2009)：

此處的是主題分類JSC i 和 JSC j的相似性，並且此一相似性以cosine測量主題分類間的引用情形得到。(Porter and Rafols 2009).

為了進一步了解實驗室的跨領域多樣性是否在單一論文的認知層次達成，如同上述的情形，計算單一論文的跨領域多樣性時，可以利用下面的方式：

此處的pai是此論文引用的參考文獻在期刊主題分類JSC i上的比例。進一步用實驗室發表的論文考慮實驗室的跨領域程度時，可以將所有論文的跨領域多樣性加以平均，如

此處的 #pap 是實驗室發表的論文數量。

此外，另兩種指標分別是主流引用外的主題分類比例以及不同機構的人員合作占論文全體比率，分別如下所示：

最後一種指標，先以書目耦合(bibliographic coupling) (Kessler 1963)產生論文之間的關連，計算方式如下：

此處的where #common_refsij 是論文 i 和 j 共同引用的參考文獻數量， #refsi 和 #refsj 分別是論文 i 和 j 包含的參考文獻數量。接下來以書目耦合關連建立論文網路，希望在網路上引用文獻相似的論文會聚集形成叢集。因此，接下來Blondel et al. (2008)的演算法，劃分網路成論文的叢集。整個方法可參見Grauwin and Jensen (2011)，結果共劃分成250個叢集。然後以下面的方式計算實驗室在認知叢集上的多樣性

此處的 p_i 和 p_j 分別是實驗室的論文屬於叢集 i 和 j 的比例。

以六種指標計算每一個實驗室的跨學科多樣性後，接下來以主成分分析(Principal Component Analysis, PCA)進行分析，四個主要的成分分別是

1) 實驗室在各種多樣性指標的綜合表現

2) 實驗室連結的學科的認知距離(cognitive distance)

3) 實驗室在實驗室層級或論文層級具有跨學科性

4) 論文發表的期刊具有跨學科的主題分類或是與其他不同機構的實驗室合作。

Interdisciplinarity is as trendy as it is difficult to define. Instead of trying to capture a multidimensional object with a single indicator, we propose six indicators, combining three different operationalizations of a discipline, two levels (article or laboratory) of integration of these disciplines and two measures of interdisciplinary diversity.

Interdisciplinarity means, at the most generic level, some degree of integration of different disciplines (Weingart and Stehr 2000; Porter and Rafols 2009; Marcovich and Shinn 2011; Wagner et al. 2011; Rafols et al. 2012).

To transform this idea into quantitative indicators, we need to answer three questions:

1. How to define a discipline?

2. At what level the integration is achieved?

3. What is the degree of disciplinary linkage achieved?

There are several ways to define a discipline from a scientometrics’ point of view. Since we are dealing with CNRS labs, the most natural would seem to use the disciplinary organization of CNRS in 10 ‘‘institutes’’ and 40 subdisciplinary ‘‘sections’’. A convenient alternative is to use the 224 Journal Subject Categories (JSCs) used by Web of Science (WoS). Finally, instead of using institutionally predefined divisions of science, one could use a more bottom-up definition of ‘‘cognitive clusters’’. To obtain these clusters, we use the roughly 300,000 French articles published between 2007 and 2010 and group them into ‘‘cognitive clusters’’ using clustering algorithms based on shared references.

In this paper, we will use three definitions of ‘‘discipline’’ and two integration levels (laboratory and article) to calculate six partial interdisciplinary indicators.

We adopt Stirling’s (2007) approach to capture the different facets of diversity : ‘variety’, ‘balance’ and ‘disparity’.

‘Variety’ characterizes the number of different categories, ‘balance’ characterizes the evenness of the distribution over these categories and ‘disparity’ characterizes the difference among the categories, usually based on some distance.

A simple indicator of the spread of the disciplines where a laboratory publishes is given by:

where pi is the proportion of articles of the laboratory in JSCi.

As we would like to include the idea of ‘‘distance’’ between disciplines, we calculate the diversity indicator (Stirling 2007; Porter and Rafols 2009) which combines both the spread of the disciplines through the pi and the distance between them.

where sij is the cosine measure of similarity between JSCs i and j. Practically, sij is measured through the citations from publications in JSCsi to publications in JSC j (Porter and Rafols 2009).

To further characterize a lab’s interdisciplinarity, it is useful to introduce an indicator of the interdisciplinarity of single articles, to test whether interdisciplinarity is achieved at this cognitive level.

Specifically, the interdisciplinary diversity of a single article is calculated as:

where pai is the proportion of articles’ references in JSCi.

To quantify the interdisciplinarity of the papers published by a lab, we aggregate the articles’ diversity indicator art_div_corr at the laboratory level by averaging over all the articles published by that laboratory:

where #pap is the number of articles of the lab for which at least one reference was identified.

Then, we choose a threshold to define the most common JSCs for each institute. ... We therefore choose a threshold value of 90 %. ... Then, for each laboratory, we count the percentage of articles outside this 90 % list and normalize by the expected value, i.e. the average value 0.1.

whereare the frequencies of the JSCs that do not belong to the Institute’s JSC main list.

Interdisciplinary collaborations can also be detected by copublications between scientists belonging to different CNRS Institutes. We compute a fifth indicator by calculating the proportion of a lab’s publications that involve authors from other Institutes

where the sum counts the number of articles of the lab involving at least two institutes and
#articles is the total number of articles published by the laboratory.

To build these ‘‘cognitive disciplines’’, we use bibliographic coupling (BC) (Kessler 1963) between the 300,000 papers published by French laboratories in the period 2007–2010 and compiled by the WoS.

where #common_refsij is the number of common references for articles i and j, and #refsi,
#refsj are the numbers of references of articles i and j, respectively.

In comparison to a co-citation link (which is the usual measure of articles’ similarity), BC offers two advantages: it allows to map recent papers (which have not yet been cited) and it deals with all published papers (whether cited or not).

This reinforcement facilitates the partition of the network into meaningful groups of cohesive articles, or clusters. A widely used criterion to measure the quality of a partition is the modularity function (Fortunato and Barthe´lemy 2007), which is roughly is the number of edges ‘inside clusters’ (as opposed to ‘between clusters’), minus the expected number of such edges if the partition were randomly produced. We compute the graph partition using the efficient heuristic algorithm presented in (Blondel et al. 2008). The whole method is described in (Grauwin and Jensen 2011).

Applying this algorithm yields in a partition of French papers into roughly 250 clusters containing more than 100 papers each.

where p_i is and p_j are the proportions of the labs’ papers belonging to clusters i and j respectively.

On average, articles refer to papers from almost 10 different disciplines (9.8 JSC). .... However, when considering those JSC that are used in more than 10 % of the reference list, this average drops to 2.7. This means that, on average, an article spreads its references on 3 main JSCs and 7 additional which benefit from roughly a single reference.

An average laboratory publishes in journals belonging to 34 different JSCs ...

PCA1: combined interdisciplinarity The main axis represents a combination of the various interdisciplinarity indicators.

PCA2: short or long cognitive distance This axis distinguishes those labs that connect distant or nearby disciplines.

PCA3: article or laboratory interdisciplinarity This axis distinguishes labs that achieve interdisciplinarity either at the laboratory or article level.

PCA4: diversity of publications’ JSCs or diversity of collaborations This axis distinguishes labs that publish in journals belonging to different JSCs (high lab_jsc_bal) from labs that co-publish with labs from different CNRS Institutes (high lab_inst_cop_bal).

We have computed the six indicators for the 680 laboratories which have published more than 50 papers over 2007–2010. To allow comparisons and statistical analysis, since the absolute values have no intrinsic meaning, we have scaled all the values to achieve an average value of 0 and a variance of 1. We then carried out a principal component analysis of the (680 9 6) matrix using the free software R (www.r-project.org/). More precisely, we used prcomp from the ‘stats’ package, without any axes rotation.

First, let us note that using the first four PCA axes gives an overall view about the interdisciplinarity practices of each lab. This view has been compared to expert knowledge, namely scientists working in those labs or scientific advisors from CNRS. This comparison, carried out for about 20 different labs from all the disciplines, suggests that these indicators characterize interdisciplinarity
in a meaningful way.

A major drawback of our method is that we cannot distinguish real interdisciplinary collaborations, giving rise to new concepts or to a coherent new scientific field, from simple pluridisciplinary practices that merely juxtapose different disciplines, as when historians use characterizing tools from physics. It seems difficult to learn much about the cognitive dimensions of interdisciplinarity from an automatic analysis of metadata of the papers.

Wouters, P., & Leydesdorff, L. (1994). Has Price's dream come true: Is scientometrics a hard science?. Scientometrics, 31(2), 193-222.

Wouters, P., & Leydesdorff, L. (1994). Has Price's dream come true: Is scientometrics a hard science?. Scientometrics, 31(2), 193-222.

本研究利用Scientometrics期刊論文以及其參考文獻為研究資料，根據多種資訊判斷科學計量學領域是否已經是硬科學，並分析這個領域的其他特性。本研究所使用的科學計量學資訊有引用文獻的相對年齡(relative age of the cited literature)、論文作者間的關係、論文題名的詞語模式(patterns of words  in the titles of these articles)等。

根據Price的知識增長理論(theory of knowledge growth)，科學家會引用本身領域的文獻，因此，如果有研究前沿(research fronts)存在於這個領域，便會產生立即效應。Price指標(Price index)可以測量立即效應(immediacy effect)，Price指標較大表示引用文獻的相對年齡較低，例如Price(1970)測得生物化學和物理的Price指標值約在60%到70%，社會科學大約在42%附近。Crane(1972)則認為科學會形成作者間彼此緊密相連的社群，因此本研究分析作者間的合著關係和引用的關係，並且利用網絡分析技術探討科學社群的凝聚程度，並且測量作者在網絡的位置連結性以及結構的相似性，根據這些資訊進行叢集，集結彼此間連結性強的作者形成一個叢集，或是形成位置相似的作者叢集。另外，Rip and Courtial (1984)和Leydesdorff (1989a)
指出題名上的詞語可視為是出版品的認知訊息(cognitive message)的指標，詞語在題名上的共現可視為是詞語間關係存在的紀錄，因此本研究也利用網絡分析技術探討詞語的共現網絡。

研究結果發現分析的779筆Scientometrics期刊論文資料，除了前三年快速的增加外，平均每年增加3.5筆，並且這些論文資料共包含12341筆參考文獻，平均每篇論文有15.8筆參考文獻。各項指標都相當穩定。Price指標的平均值為43.0%，若以每年的Price指標的平均值在34.0%到51.4%之間。

以作者資料來看， 779筆論文資料共計由669位不同的作者完成，有接近3/4的作者(488位)僅出現在一筆論文資料上，每位作者平均出現在1.8筆論文資料上，其作者生產力符合Lotka分布，並且大部分(61%)的論文是單一作者，平均每篇論文有1.6位作者。合著作者的論文資料中，大多數的作者都僅和一到兩位同事合作，合著網絡相當破散，但幾個較大的網絡與作者在同一機構任職、參與同一研究計畫或者具有共同的研究興趣有關。

Scientometrics期刊論文的作者引用網絡則呈現高度凝聚的狀態。779筆論文資料中有441筆被其他Scientometrics期刊論文引用，每筆Scientometrics期刊上的論文引用的論文平均有19.4%同樣是Scientometrics期刊的論文。發表超過1篇以上論文的作者共有181位，其中的130位作者有引用其他129位作者的資料，利用作者之間的彼此互相引用關係，發現形成的集團(clique)大多與作者任職機構有關，也有一個集團是成員間曾彼此辯論(debate)而產生。最後，題名上的詞語共現網絡也同樣有高度凝聚的情形。從上面的資訊可以判斷科學計量學領域已經由多種的學科背景在認知與社會性上整合而成，但並沒有發現研究前沿的現象。

In more than one respect, Scientometrics displays the characteristics of a social science journal. Its Price Index amounts to 43.0 percent, and is remarkably stable over time.

The majority of the published items in Scientometrics has been written by a single author. Moreover, the network of co-authorships is highly fragmented: most authors cooperate with no more than one or two colleagues.

Both the citation networks of the authors and the network of title words indicate that the field is nonetheless highly cohesive.

The characteristics of the publications in this journal, and the patterns of the bibliometric relations among them, may therefore indicate the type and extent of the cognitive and social integration of the various disciplinary backgrounds into scientometrics as a field.

The question, in other words, is how "hard" scientometrics is, and how strongly its knowledge is codified. These properties can be measured in terms of:
a) the relative age of the cited literature, the so-called "Price Index",
b) the relations among the authors of articles published in Scientometrics; and
c) the pattern of words in the titles of these articles.

According to Price's theory of knowledge growth (Price 1965), science distinguishes itself from other fields of study by the way scientists refer to their literature (Price 1970). The existence of "research fronts" in science supposedly leads to an "immediacy effect", which can be measured in terms of the so-called "Price Index".

The Price Index is defined as "the proportion of the references that are to the last five years of literature" (Price 1970). Price estimated that this index would vary between 22 and 39 percent if no immediacy effect were present. [1] A field that was all research front and with no general archive might have a Price Index of 75 to 80 percent.

From his analysis of 162 journals, Price (1970) concluded: "Perhaps the most important finding I have to offer is that the hierarchy of Price's Index seems to correspond very well with what we intuit as hard science, soft science, and nonscience as we descend the scale." Biochemistry and physics are at the top, with indexes of 60 to 70 percent, the social sciences cluster around 42 percent, and the humanities fall in the range of 10 to 30 percent.

Science is, on the whole, practised in tightly knit communities in which the authors address one another (Crane 1972).

Co-authorship relations can be considered as indicators of co-operation. [3]

The meaning of citation relations is less clear, given the ongoing citation debate (MacRoberts and MacRoberts 1989; Cozzens 1989; Luukkonen 1990; Leydesdorff and Amsterdamska 1990; Woolgar 1991). But whatever the precise meanings of citations may be, citations can be considered as sociometric data, and the resulting network can accordingly be analyzed (cf. Shrum and Mullins 1988).

We analyzed the extent to which the authors are connected to one another, i.e. the cohesiveness of the network, as well as the pattern displayed by each author in relation to all other authors, i.e. the position of authors in the network.

We also analyzed the similarities among authors in both these dimensions of the matrices, i.e. we clustered strongly connected authors as well as authors in similar positions. Direct as well as indirect linkages between the authors are involved in this analysis.

Strong cliques are sets of authors connected by relations in such a way that all members of the clique are connected to one another, and anyone for whom this holds is included in the clique. The inclusion criterion is less strong for weak cliques, in which all pairs within the clique must have relationships with all other pairs, and anyone with a relation to or from a member of the clique is included.

Strong structural equivalence clusters are sets of authors with completely identical positions in the network (the distance dP between them is zero). Weak structural clusters are sets of authors with a significant similarity in their patterns of relations (the distance dP is small).

As noted, we wished to know whether a structurally codified semantics of scientometrics exists or whether, on the contrary, the articles in Scientometrics use the different terminologies of the various disciplines surrounding scientometrics.

Given the functions of titles of articles, the words in these titles can be considered as indicators of the cognitive message of the publication (Rip and Courtial 1984; Leydesdorff 1989a). The co-occurrence of words in titles can be considered as an indication of the existence or non-existence of relations between these words (Callon et al. 1983).

Since 1978, 779 items have been published in Scientometrics. They contain 12,341 references to the scientific literature. [10]

The number of publications per year in the journal increases in a linear way (Fig. 1). [11] After a steep growth during the first three years, the number increases by 3.5 publications per year.

The number of references per year shows a comparable pattern, although somewhat more irregular. Every publication contains on average 15.8 references (cf. Yitzhala, 1991). Since 1986, this number has become stable at an average of 15 references per publication (Fig. 2).

The publications in Scientometrics were written by 669 different authors. On average, every author published 1.8 times and every paper was written by 1.6 authors. Nearly three-fourth of the authors (488 or 73 percent) published only once in Scientometrics. The distribution of productivity among the authors is a Lotka distribution (Fig. 4).

The average Price Index of Scientometrics is 43.0 percent. ... The Price Index varies between 34.0 and 51.4 percent (Fig. 5). The regression line is not significant. [12] Apparently, the index displays neither rise nor fall since 1978.

Recently, Schubert and Maczelka (1993) concluded from an analysis of Scientomettics in 1980-81 and 1990-91 that the journal has moved slightly from the "soft" (social) towards the "harder" (natural) sciences. They drew this conclusion from the rise of the Price Index from 35 percent to 42 percent between these measurement points. This observation is, however, based on only two measurements. Because of the statistical fluctuations in the value of the Price Index over time, any conclusion can be drawn regarding the development of the Price Index if one restricts oneself to only two measurement points.

In accordance with Price's theory, the number of references to literature of a specific age rises until the cited literature is two years older than the citing literature, and then falls off (Fig. 7). Note that this decline is gradual. Apparently, only a small "immediacy effect" is visible in scientometrics.

A general phenomenon in science is the growth of the number of co-authored scientific articles, relative to the total scientific production (Luukkonen et al. 1992; Abt 1992).

In Scientometrics, however, 61 percent of the articles have been written by a single author. This share is stable over time.

The network of co-authorships is highly fragmented. ... With the exception of three subgroups, most co-authors cooperate with no more than one or two colleagues.

Comparison of the composition of the weak structural equivalence clusters with the relational cliques reveals that two clusters are identical: a group of authors from Leiden (Van Raan et al.) and a group of authors with various institutional affiliations, probably best characterized as the "co-word analysis group". So, these two groups have distinct identities, with respect both to their relations and to their positions in the network.

Some clusters seem constituted by the institutional affiliations of the authors. This holds for the Leiden group and for the authors around ISI (cluster 3). In other cases, nationality appears to be the binding force. This holds for the group in Hungary (cluster 5), the Belgian informetricians (cluster 10) and the Spanish scientometricians (cluster 6). However, cluster 1 can best be characterized by its research program (co-word analysis). Cluster 2 seems to consist of authors from Sussex together with CHI Research Inc. Thus, co-author relations are not only institutionally defined; shared interests and common intellectual goals play a role as well.

To sum up, scientometrics is a fragmentary field of co-authorships. The authors are highly selective in their co-authorship relations with one another. Co-authorships are defined neither exclusively by social nor only by intellectual factors. Both dimensions shape the pattern of co-authorships.

With respect to the number of solitary authors and the large number of isolated small clusters, scientometrics exhibits the pattern of a social science.

Of the 779 articles published in Scientometrics, 411 were subsequently cited one or more times in Scientometrics. The share of references to Scientometrics (as a percentage of all references) has stabilized around an average of 19.4 percent since 1987.

Of the 181 authors in the core set, 130 authors cite one another. So, 51 (or 28.2 percent) of the authors publishing more than one article in Scientometrics from 1978 till 1993 are neither citing nor cited within this group of authors.

The core set of authors in Scientometrics is found to be highly cohesive in terms of their mutual citation relations. All these authors are members of one single weak clique. Moreover, a majority of these authors (88) also belongs to one strong clique (Table 5).

The picture is different if we exclude all indirect relations from the analysis. This "fine structure" of the citation matrix is shown in Table 6, where 13 strong cliques and 6 weak cliques are revealed. Most strong cliques seem to coincide with shared institutional affiliations. The exception is clique 9, which indicates the existence of a debate among the members of this clique.

The most striking feature of the network of title words of articles published in Scientometrics is its cohesiveness. All words cluster together in a single strong component clique (Table 8). If only direct relations are included, all words cluster together in a single weak component clique. This means that all words are either used together in a title or share a common co-word.

Thus, the language of scientometrics is both strongly unified and weakly codified. This strong cohesiveness is a stable characteristic of the titles in Scientornetrics, from the very start of the journal. Perhaps a distinct discourse already existed before the journal was founded. In any case, it constitutes a textual identity of scientometrics as a field, one probably different from the various mother disciplines. Thus a process of de-differentiation seems to have occurred not only in the patterns of citing (and being cited) but also at the cognitive level.

The interpretation of the Price Index is complicated because of these variations within disciplines. If we, nevertheless, take the Price Index preliminary as an indicator of "hardness", scientometrics belongs to the group of relatively hard social sciences. At the same time, it stays unequivocally within the social science range. Taken literally, Price's dream has therefore not come true, since he postulated the emergence of a completely new type of social science with a natural science character. But if we reformulate his goal a posteriori in a more modest way, as the building of a relatively hard social science, it did come true.

The value of the Price Index appears stable over the years. Since a number of other indicators also exhibit stability, this seems to suggest the existence of some scientometric identity. For example, the journal expands at a regular rate, while the percentage of co-authored papers increases only very slowly. The origin of this stability can best be explained by the finding that the community of researchers who have published more than once in Scientometrics acts as a tightly knit network.

In addition to the co-authorships within various institutes, and partly overlapping with this structures, there are national co-authorship relations, like those among the Belgian informetricians, and programmatic co-authorship relations, like those among the users of the French co-word instrument. In general, co-authorship relations are firmly embedded in existing social structures, both at the national and at the community level.

These various strong graphs of co-authors, however, are structurally embedded in the communication structure as indicated by textual indicators. Both in terms of citation relations and in terms of title-words the network is very cohesive, while the structural dimensions of codification are less clear.

In summary, the community of authors publishing in Scientometrics is well integrated, while there are no indications of an exclusive paradigm or a research front.

Schubert, A. (2002). The web of scientometrics: A statistical overview of the first 50 volumes of the journal. Scientometrics, 53(1), 3-20.

Schubert, A. (2002). The web of scientometrics: A statistical overview of the first 50 volumes of the journal. Scientometrics, 53(1), 3-20.

Schoepflin and Glänzel (2001)將Scientometrics期刊上的論文主題分為六類：1. 理論(包括書目計量學理論、數學模型和書目計量學定律的公式化)、2. 案例(案例研究和實務論文)、3. 方法學與應用、4. 指標 (指標工程與資料呈現)、5. 社會學取向(書目計量學的社會學方法和科學社會學)以及6. 政策研究(包括科學政策、科學管理和一般與科技討論)等，並應用這樣的分類討論Scientometrics期刊的論文主題在1980、1989及1997等三個不同年份的比重變化。上述的主題可以在歸納成核心的書目計量學(core bibliometrics) (2, 3, 4)和背景研究(background research) (1, 5, 6)或是理論研究(1, 3, 5)和應用研究(2, 4, 6)。Schoepflin and Glänzel (2001)的研究發現案例與方法學有明顯與穩定的成長，但社會學取向和科學政策的論文數量減少。

本研究以前50卷1443篇Scientometrics期刊的論文資料進行計量分析，這1443篇論文上包含來自60個國家的1223位作者，共包含25200個參考文獻(不重複的項目共16500個)，除了382篇論文不曾被引用外，1061篇曾被引用的論文共被引用7242次。

以合作關係的分析，55.1%的論文為單一作者，只有5.4%的論文由3位以上的作者合作完成，論文的平均作者數是1.61，過去十年來合作的情形略有增加，因此科學計量學領域比較像社會科學或數學。國際合作情形較罕見，只有 7%的Scientometrics論文由一個以上的國家合作完成，但後25卷的國際合作情形是前25卷的兩倍以上。

以Price指標(the Price index)分析Scientometrics論文的25200個參考文獻，了解其引用文獻在五年內出版的比例，藉以判斷該期刊是屬於軟科學(soft sciences)或硬科學(hard sciences)，結果發現在五年內出版的文獻大約占45%。其引用的期刊來源，除了圖書資訊學(Information Science & Library Science)、電腦科學(Computer Science)和跨領域應用(Interdisciplinary Applications)外，其餘多屬普通物理(general physics)、普通化學(general chemistry)、普通醫學(general medicine)等較廣泛的領域。但也可以發現有相當高比例(13.6%)是期刊自我引用的情形，就被引用的情形來看則高達47.3%是來自期刊本身。

A total of 1443 items were published by 1223 authors from 60 countries. They contained 25200 references to about 16500 different items ...1061 Scientometrics papers received 7242 citations during the 1978-2000 period (i.e., 382 papers remained uncited).

Activity Indexes show even more spectacularly the outstanding relative activity of a few countries (first of all Hungary, but also Belgium, Bulgaria, Chile, Mexico, Netherlands and, if measured against social science standards, then P.R. China, Poland, Russia and Spain, as well). A conspicuously low relative activity is shown by Italy and Japan (not so much if social science standards are concerned); interestingly, most English-speaking countries (US, England, Australia, Canada) exhibit a lower-than-average activity.

In their paper, Schoepflin and Glänzel (2001) classified the papers published in Scientometrics into six thematic categories, and studied the change in the weight of these categories by selecting three sample years: 1980, 1989 and 1997.
They used the following categories:
1. (THEO) Bibliometric theory, mathematical models and formalisation of bibliometric laws;
2. (CASE) Case studies and empirical papers;
3. (METH) Methodological papers including applications;
4. (INDI) Indicator engineering and data presentation;
5. (SOCI) Sociological approach to bibliometrics, sociology of science;
6. (POLI) Science policy, science management and general or technical discussions.

The classification permitted to group the material in several ways: the categories can be regarded from the viewpoint of core bibliometrics (2, 3, and 4) and background research (1, 5, and 6), but also with respect to theoretical (1, 3, and 5) and applied research (2, 4, and 6).

There are two obvious developments: an impressing and steady growth of case studies (Category 2) and methodology (Category 3) and the loss of position of articles on sociological (Category 5) and science policy (Category 6) issues.

In this respect, however, scientometrics resembles rather to the social sciences(or, maybe, mathematics) than to the sciences: 55.1% of the papers published in the first 50 volumes of Scientometrics is single-authored and only 5.4% of them are multi-authored (more than 3 authors). The average number of authors per paper is 1.61. In the past decade, nevertheless, there is a slight tendency of growing collaboration (see Figure 3).

International collaboration is even less favourised in the scientometrics community. There is a modest 7% of Scientometrics papers having more than one country in the authors’ affiliation section in the by-line of the publication. Nevertheless, the tendency is unambiguous: the fraction of internationally co-authored papers more than doubled from the first to the second 25 volumes.

The 25200 references of the papers form, as it were, the intellectual “hinterland” of research reported in Scientometrics. Clearly, they constitute a vast treasury of information about the history, sociology, epistemology of the field and its journal, and several attempts were made to make the most of this information (Schubert and Maczelka, 1993; Wouters and Leydesdorff, 1994; Schoepflin and Glänzel, 2001).

De Solla Price (1970) introduced an index, later named after him, with the aim of distinguishing between “harder” and “softer” sciences. The Price Index is defined as the percentage share of references to items not older than five years at the time of publishing the citing paper. Typical “soft science” journals (German Review, American Literature, Studies in English Literature, Isis, in Price’s original study) have an index value less than 10%, while, e.g., some research front physics journals may reach 80%.

The Price Index of the journal Scientometrics is around 45%, i.e., it occupies a medium position on the hardness scale.

Among the highly cited sources there is a clear dominance of SCI/SSCI-covered titles: 19 of the 25 titles belongs to this category. References to the journal itself (journal self-references) constitute 13.6% of all references – it is a typical value for a consolidated primary journal.

The journal Scientometrics itself is categorised into two subfields: Information Science & Library Science and Computer Science, Interdisciplinary Applications.

It can be seen that Information Science & Library Science would remain the main source of information for the journal even if self-references were disregarded, while Computer Science, Interdisciplinary Applications would disappear from the chart without them.

Among science journals, those from broader-scope subfields (general physics, general chemistry, general medicine, multidisciplinary sciences) contribute the most to the reference base of Scientometrics. The presence of Analytical Chemistry among the top cited fields may be connected with the fact that this is the original and main fireld of the Editor-in-Chief of the journal.

The journal self-citation rate of 47.3% is rather high, particularly if compared with the self-reference rate of 13.6%. It indicated that the “outside world” pays less attention to the journal than vice versa.

Dutt, B., Garg, K. C., & Bali, A. (2003). Scientometrics of the international journal Scientometrics. Scientometrics, 56(1), 81-93.

Dutt, B., Garg, K. C., & Bali, A. (2003). Scientometrics of the international journal Scientometrics. Scientometrics, 56(1), 81-93.

過去關於科學計量領域的計量分析結果：Wouters and Leydesdorff (1994)根據Price指標的分類，指出科學計量學並未成為一門硬性的社會科學(hard social science)，Schoepflin and Glänzel (2001)則認為這個領域的異質性很高，每一個次領域都有它本身的特性。

本研究針對以下的問題進行探討：確認Scientometrics期刊上1978到2001年發表論文資料的主題，分析這期間論文的分布情形，不同國家在不同主題上的貢獻，具有主要生產力的機構，並藉由合著關係發掘國內與國際間的合作情形。本研究將論文的主題分為科學計量評估(scientometric assessment)、引用與叢集分析(citation and cluster analysis)、科學計量分布(scientometric distribution)、科學的歷史(history of science)、科學合作(scientific collaboration)、科學計量學的理論研究(theoretical studies on scientometrics)，不在上述主題的論文則歸類為其他。

結果發現：論文數最多的主題是科學計量評估(scientometric assessment)，這個現象反映出科學政策的制定逐漸運用科學計量工具的事實，其次是理論研究(theoretical studies)。在前期(1978-1986年)，科學的歷史(history of science)方面的論文較多，其次是引用與叢集分析(citation and cluster analysis)；科學計量分布(scientometric distribution)在前期與中期(1987-1994年)都相當重要，但後期(1994-2001)逐漸減少；後期具有最重要地位的主題則是科學合作(scientific collaboration)。

美國是目前生產力最高的國家，共占17.7%的論文，主要的8個歐洲國家則共佔47.6%，但美國在論文所佔的比例逐年減少，加拿大與前蘇聯有同樣的情形，但荷蘭、印度、法國和日本在上升中；從每一個機構平均發表的論文數可以看出這個領域的生產力相當分散，1317篇論文的作者資料共來自1538個機構，但是有1109篇論文是單一機構發表，兩個或以上的機構發表的論文只有208篇；在1538個機構中，發表超過15篇或以上論文的機構共有8個，匈牙利和荷蘭各有2個，其餘的4個機構分別位於印度、比利時、英國和美國；雖然目前的論文以單一作者為主，論文的平均作者數僅為1.73，但多位作者的論文雖然僅占18%，但正逐漸增加。

The study indicates that the US share of papers is constantly on the decline while that of the Netherlands, India, France and Japan is on the rise.

The research output is highly scattered as indicated by the average number of papers per institution.

The scientometric output is dominated by the single authored papers, however, multi-authored papers are gaining momentum.

However, Wouters and Leydesdorff [1] presented a combined bibliometric and social network analysis of papers published in first 25 volumes of Scientometrics, and concluded that scientometrics has not become a hard social science as reflected by the values of Price Index.

In another study, Schoepflin and Glänzel [2] point out that the field of scientometrics is heterogeneous, and each sub-discipline has its own characteristics.

The objectives of the study are:
(i) to identify the scientometric themes on which papers have been published in volumes 1(1978) to 50 (2001), and to find out as to how the emphasis on different themes have changed during different periods;
(ii) to examine the distribution of output of different countries during 1978 -2001, and to analyse the change in the trend, if any;
(iii) to study the relative research emphasis of different countries on different scientometric themes;
(iv) to identify the most productive institutions, and to study the scientometric themes they have dealt with;
(v) to study the pattern of co-authorship and the pattern of domestic as well as international collaboration.

The entire data set was classified into seven groups:
scientometric assessment;
citation and cluster analysis;
scientometric distribution;
history of science;
scientific collaboration;
theoretical studies on scientometrics.
Papers which could not fit into these categories were kept under ‘others’.

An analysis of the data indicates that about one-third of the papers published in Scientometrics deal with scientometric assessment which mainly include cross-national, national and institutional assessment, besides evaluation of journals, bibliometric performance indicators, funding and performance, and S&T indicators. This was followed by theoretical studies (Table 1).

From the values of the Activity Index presented in Table 1, it is observed that the priorities of different themes kept changing during different periods. For instance, during 1978-1986 ‘history of science’ followed by ‘citation and cluster analysis’ were the areas of maximum emphasis.

Studies dealing with ‘scientometrics distribution’ got almost the same priority during 1978-1986 and 1987-1994, but emphasis on this theme has gone down considerably in the last block.

During 1994-2001, studies dealing with ‘scientific collaboration’ got maximum priority followed by ‘scientomeric assessment’.

Major contribution (>=2%) of the total output came from 13 countries listed in Table 2. The distribution of papers presented in Table 2 indicates that USA tops the list of publications which are 17.7 per cent of the total world output.

The values of the Activity Index for different countries (Table2) indicate that during the last two blocks, i.e. 1987-1994 and 1994-2001, the productivity of the USA has declined considerably. Similar is the case with Canada and the former USSR.

Further analysis of data presented in Table 2 indicates that Scientometrics is getting Euro-centred, as 8 countries of Europe listed in Table 2 have contributed 47.6 per cent of the total output. The share may be greater, if the output from other European countries not listed in Table 2 is included.

The total output of 1317 papers published in 50 volumes of Scientometrics came from 1538 institutions. 1109 papers were published involving only a single institute and the rest 208 involved collaboration either with 2 or more institutes.

Number of such institutes which published 15 or more papers is only 8 and their share in the total output is 259 (19.66 %). Of the 8 prolific institutions, two are from Hungary, two from the Netherlands, and one each from India, Belgium, UK and USA.

The results presented in Table 5 indicate that slightly more than half of the papers were single authored and the rest were written by either two or more authors. The share of multi-authored papers (>=3) is much less (18%) only as compared to single or two authored papers.

A study carried out by Cunningham and Dillon [7] for authorship pattern in library and information science indicates average number of authors per paper for information science is 1.17. In scientometrics the average number of authors per paper is 1.73 which indicates a better collaboration than library and information science.

The values of DCI for Spain, France, India and Japan were much higher than the world average indicating a good domestic collaboration. However, except Spain all these countries had very low values of ICI, which indicates that these countries have a poor international collaboration. On the other hand UK, Hungary, Belgium, Canada and Germany had good international collaboration as reflected by the values of ICI.

The focus of scientometric studies is shifting from the history of science and scientometrics distribution to scientific collaboration and scientometric assessment.

Scientometric assessment constitutes about 34% of the total output of the papers which is the highest among all the themes. Emphasis on scientometric assessment studies reflects the growing realisation of its utility as a tool for science policy making.

van den Besselaar, P. (2001). The cognitive and the social structure of STS. Scientometrics, 51(2), 441-460.

van den Besselaar, P. (2001). The cognitive and the social structure of STS. Scientometrics, 51(2), 441-460.

本研究利用作者共被引分析(author cocitation analysis)分析STS領域的社會結構，探討做為次領域間連結的作者或研究機構。本研究將STS領域分為STS的量化研究次領域(the qualitative STS sub-field)、STS的質性研究次領域(the qualitative STS sub-field)和政策導向次領域(the policy oriented sub-field)，並且以Scientometrics期刊為STS的量化研究的代表，Social Studies of Science和Science, Technology and Human Values兩種期刊代表STS的質性研究，Research Policy則是STS政策研究的代表。針對1986到1997年間在這些期刊上被引用超過25次的229位作者，建立他們的共被引矩陣，然後進行因素分析(factor analysis)，查看這些作者被歸類的情形，並且與上述的次領域進行比較分析。此外，本研究也探討被不同次領域引用的作者、不同次領域之間的作者的合作關係以及有多少位作者在不同的次領域發表論文？

Table 1表示762、305、304及569位作者分別曾在Scientometrics、Social Studies of Science、Science, Technology and Human Values以及Research Policy等期刊發表論文，Scientometrics和Research Policy的作者平均在對應的期刊上發表1.5及1.7篇，比Social Studies of Science和Science, Technology and Human Values的1.1篇來得高。曾在四種期刊發表論文的作者則是1756位，平均每位作者發表的論文數為1.4。

共有759個機構曾在四種期刊上發表論文，但只有少數的機構有較高的生產力，例如超過11篇論文的機構僅有41個。此外，從Table 2也可以發現有些高生產力機構的論文是在不同次領域的期刊上發表。

共有65個國家在四種期刊上發表論文，其中大多數的國家(57個)有在Scientometrics上發表，但其他三種期刊都僅有約半數的國家有發表的紀錄。

將作者共被引矩陣進行因素分析後，較大的因素共有7個，依作者撰寫論文的內容將各因素命名。其中第1個因素和第6個因素間有很大的關係，第1個因素有大半數的作者的次高負荷是落在第6個因素上，反之亦然，第1個因素和第6個因素的研究主題為科技政策相關的STS研究。第2個因素的研究主題為STS的質性研究。第3個因素和第4個因素、第5個因素以及第7個因素彼此間的作者有關係，這些因素可以視為是STS的量化研究，進一步來說，第4個因素、第5個因素和第7個因素的主題分別是科學社會學(Sociology of Science)、詞語共現分析和資訊計量學。

接下來，Table 4 分析各次領域的專家(specialists)以及兼通兩門或以上的通才(generalists)。本研究將專家定義為在該次領域發表的論文數超過該領域論文總數0.69%以上的作者，STS的量化研究、質性研究和政策導向研究等次領域各有31、23和41位。量化研究次領域的專家並且也發表質性研究相關論文的作者有6位，反之質性研究次領域的專家並且也發表量化研究相關論文的作者只有2位。量化研究次領域的專家同時發表政策導向相關論文的作者有14位，政策導向研究次領域的專家並且也發表量化研究相關論文的作者則有11位。從以上數據顯示，量化研究與其他兩個次領域的關係主要是由量化研究次領域的研究者在維繫著，也就是量化研究次領域的研究者是主要的跨邊界者(boundary spanners)。

Table 4上也可以發現一些從質性研究次領域跨越政策導向研究的研究者，這個研究結果修正了先前認為質性研究次領域比較獨立的看法。

The differentiation of scientific fields into sub-fields can be studied on the level of the ‘scientific content’ of the sub-field, that is on the level of the products, as well as on the level of the ‘social structures’ of the sub-field, that is on the level of the producers of the content.

By comparing the behavior of the constructs with the behavior of the constructors, we are able to demonstrate the analytical distinction between a cognitive and a social approach in an empirical way.

Although we are able to distinguish analytically between the cognitive and social dimension of the development of the research field, we find similar patterns of differentiation on the social level too. At the same time, this differentiation differs in some respects from the cognitive differentiation pattern.

Consequently, the social and the cognitive dimensions of the STS field are not independent – as no serious STS scholar would argue – but also not identical, as radical constructivists claim, but are strongly interacting.

It was claimed that scientometrics has to focus more on the role it can play for qualitative STS, and that scientometric researchers should refrain from sterile data and mathematics. It was felt that scientometric results have to be carefully interpreted from a substantial perspective, to be meaningful for S&T policy.

There, we showed that the journals Social Studies of Science (SSS) and Science, Technology and Human Values (STHV) form a reasonable operationalization of the qualitative STS sub-field. Research Policy represents the policy oriented sub-field, and Scientometrics can be used as a representation of the quantitative STS sub-field. These journals are central in STS as they have the highest impact factors in their respective sub-fields.

In this paper we will use the same boundary of STS to analyze the social structure of the field: who are the authors and what are the research groups in the field as defined by the mentioned journals? Do they function as the ties between the various sub-fields?

Data about authors and institutional affiliation can be found on the CD-ROM version of the Social Science Citation Index (SSCI). We downloaded the full records for all publications in the four journals for the period 1986-1997.* This resulted in a database with 3579 records. ... Finally, as is usual in scientometric studies, for further analysis we restricted the database to Articles, Reviews, Notes, and Letters, and excluded other document types. This resulted in a final set of 1787 documents.

Referring to a text may indicate the use of a knowledge claim to support one’s own position, or to oppose to. Referring to persons, on the other hand, may indicate the existence of a social relationship. Therefore we will use author co-citation analysis as a first methodology to analyze the social structure of the STS field. In this way, we will describe the STS field in terms of clusters of authors that are placed near each other by the scholars active in the field.

Using the prepared database and bibexcel, an author co-citation matrix has been produced of all cited 229 authors with more than 25 citations over the 1986-1997 period. Factor-analyzing (principal component analysis, varimax rotation with Kaiser normalization) this matrix results in clusters of authors, and the question is whether these clusters differ from the three sub-fields of qualitative, quantitative, and policy oriented STS.

If a communication system shows considerable segregation, individual researchers (or institutes) could play the role as weak ties [3] between the sub-fields.

(i) Authors can refer to materials from other sub-fields. We classify these authors as being active on the borders of the sub-fields. The border between sub-fields A and B is then defined as the authors of papers in sub-field A referring to papers in sub-field B, and the other way around. How densely populated are the borders between the subfields?

(ii) Authors can cooperate with colleagues active in the other sub-fields. Even if authors specialize, research groups and institutions may cover more sub-fields, and this could indicate social integration of the field on a more informal level of communication.

(iii) Generalist authors work in various sub-fields. Do many authors publish in more than one sub-field, or do we see a specialization and differentiation on the level of individual scholars? How many generalists can be found among researchers and institutions? The larger numbers we find, the stronger is the degree of communication between the sub-fields.



The average number of authors per article is 1.4, but this figure is higher in Scientometrics (1.5) and in Research Policy (1.7), but considerable lower (1.1) in the two qualitative STS journals.



As expected, the number of frequently publishing institutes is rather small, compared to the grand total.

If we aggregate one more step, to the level of countries, we find 65 countries active in the STS field, of which some 57 are active within scientometrics. However, only half of the countries are publishing in the qualitative journals SSS and STHV. The same is true for Research Policy.

Factor analyzing the author co-citation matrix resulted in a solution of 22 factors with an eigenvalue larger than 1. Inspecting the scree plot shows that seven factors dominate the structure, and these factors explain more than 70% of the total variance. More than 90% of the 220 cited authors have their highest factor score on one of these seven factors.



The authors in Factor 1 are within science & technology policy studies and in research & innovation management studies, or in related fields in management and economics. The same holds for the small Factor 6. Half of the authors in Factor 1 have a relatively high second factor loading in Factor 6, and all authors with their highest loading on factor 6 do have a high second loading on Factor 1.

Authors with their highest factor loading on Factor 2 all belong to qualitative STS, and they generally do not load on other factors.

Factor 3 represents quantitative STS. Most authors with the highest loading on Factor 4 can be characterized as traditional sociology of science (e.g., Merton). Factor 5 represents coword analysis, and Factor 7 represents informetrics and scientometric distributions (e.g., Bradford and Lotka). Between the Factors 3, 4, 5, and 7 we find a considerable ‘interfactorial complexity’: the authors loading highest on Factor 3 often have a substantial second loading on one of the Factors 4, 5, or 7. The same is true the other way around.

Therefore I also created the author co-citation matrix of all authors with more than 25 citations over the whole period with the highest loading on the Factors 3, 4, 5, or 7. Authors that have a second loading on these factors of more than 0.2 are also included. This set of authors represents the sub-field scientometrics.

Factor-analyzing this matrix in a similar way results in seven substantial factors. Inspection of the factors shows that they represent the following research foci: Policy oriented scientometrics (Factor 1); Empirical science & technology studies (Factor 2); Coword analysis (Factor 3); Scientometric distributions (Factor 4); Critique of scientometrics (Factor 5); Patent studies (Factor 6); Economics of technical change (Factor 7). This result corroborates that the method is suited for analyzing the fine structure of research fields.

If we now summarize these findings, the factor-structure of the co-citation matrix of STS reproduces the clear split between policy oriented STS (Factor 1 plus 6), qualitative STS (Factor 2), and quantitative STS (Factors 3, 4, 5, 7), while at the same time showing some internal differentiation in the sub-field of scientometrics. In other words, the author co-citation analysis reveals a similar structure as the journal-journal citation analysis did.8

Firstly, we distinguish the groups of specialists, which consist of the authors with relatively high numbers of publications in one of the various sub-fields of STS. We consider a scholar as specialist in one of the sub-fields, if he or she is (co-) author of at least 6, 4, or 3 publications respectively in quantitative, qualitative, or policy oriented STS. In this way, the threshold is about the same in the three sub-fields: 0.77%, 0.69%, and 0.73%.

Secondly, we have the semi-generalists, the groups of authors active in two of the three sub-fields each. A semi-generalist is defined as an author who has published at least two publications in two of the three sub-fields.

Finally we have the group of generalists, publishing in all the three sub-fields, again based on at least two publications per sub-field.




The number of specialists in Scientometrics is 31, and only six of them have published in SSS or STHV. The other way around we identified only 2 authors. This implies that the more quantitative researchers maintain the relations between these two sub-fields

The number of Scientometrics authors also publishing in Research Policy is much higher, and some 45% of the scientometrics specialists also work – at least incidentally – on S&T policy topics. Researchers frequently publishing in Research Policy publish a little less (27%) in Scientometrics, but this is still a substantial number.

This underlines our earlier conclusion that research policy and management is related to scientometrics for the part of using scientometrics in research evaluation, but not much wider.8

Between Scientometrics and Research Policy, as well as between Scientometrics and SSS/STHV, most of the authors who maintain the relation have most publications in Scientometrics, and generally only a single publication in one of the other journals. This implies that the relations between the sub-fields (also the very weak one’s) are maintained to a large extent by scientometricians.

Between Research Policy and SSS/STHV the picture is more balanced, with a weak emphasis on the SSS/STHV authors. The number of authors publishing both in qualitative STS and S&T policy studies is very low, as is the number of authors publishing both in quantitative STS and in qualitative STS. Only the number of authors publishing in both quantitative STS and S&T policy studies is substantial.

Lowering the threshold increases the number of (semi-)generalists, but of course most of them have a very low number of publications, and the scientometricians are the boundary spanners, much more than the others.

However, a larger number of qualitative authors than expected is also active in the S&T policy studies. Only this latter finding modifies slightly our earlier conclusion that qualitative STS is an isolated sub-field.

We use a 3% threshold, and various organizations that exceed this threshold in one of the sub-fields are in Table 6. Three of the eight organizations are specialized in only one sub-field. Four others are specialized in two sub-fields, and only one organization is a generalist one, and active in three sub-fields.

In other words, there is a relatively low level of specialization here, as most of the institutions seem to be rather active in more sub-fields.

If we decrease the threshold to 2%, another 15 institutions count as specialists. However, of these 15 institutions only a few are active in more sub-fields. This implies that the most productive institutions within STS are also the broadest in their covering of the field.

Where the cognitive analysis showed that the relationship between scientometrics and S&T policy studies is stronger than the relations between qualitative and quantitative STS,8 on the level of the conferences (and as shown before, on the level of research institutes) it is the other way around. In other words, the institutional structures and the cognitive structures are not identical.

If we summarize the findings, we see that the cognitive patterns of integration and (mainly) differentiation to a large extent are visible within the social structure of the field.

The social relations between quantitative STS and policy oriented STS are similar to the cognitive relations between the two sub-fields. The links, however, between the two sub-fields are only between a substantial part of scientometrics and a small part of S&T policy studies, namely the part focusing on evaluation and performance studies.

The larger part of S&T policy studies is on technological innovation and on evolutionary approaches to technical change, and these research topics are not related to the research front in scientometrics, as the author co-citation analysis underlines.

Most importantly, we found that the interaction between qualitative and policy oriented STS is much stronger on the social level of authors and institutions than on the cognitive level of documents.

This may explain why the discussants in the panel session quoted earlier in this paper saw different divides, than the one’s I revealed in Ref. 8: the social structure of the STS field is not identical to its cognitive structure.

Within the mainstream of STS it is generally accepted that the production of knowledge and the grounding of knowledge claims consists of a ‘seamless web’ of cognitive and social elements.

Lu, K., & Wolfram, D. (2010). Geographic characteristics of the growth of informetrics literature 1987–2008. Journal of Informetrics, 4(4), 591-601.

Lu, K., & Wolfram, D. (2010). Geographic characteristics of the growth of informetrics literature 1987–2008. Journal of Informetrics, 4(4), 591-601.

本研究探討在地理上的生產力遷移(shifts in productivity)是否發生在書目計量學(bibliometrics)、資訊計量學(informetrics)和科學計量學(scientometrics)等計量學(metrics)領域，也就是歐洲的貢獻明顯地成長，並且北美的貢獻相對來說有減少的情形。

有關計量學的研究，Hood and Wilson (2001)和Stock and Weber(2006)等研究都分析了這個領域的文獻成長情形。Hood and Wilson (2001)回顧了計量學領域的發展，並且比較bibliometrics、scientometrics和informetrics的相關文獻，發現bibliometrics還是在相關領域上使用最廣泛的詞語。Stock and Weber(2006)從觀察中確認這個領域從1980年後便持續地成長。Wolfram (2008)則發現在計量學領域中，北美的文獻有明顯地減少而歐洲則是急遽地增加的情形。

本研究利用bibliometrics、scientometrics、informetrics、cybermetrics、webometrics、citation analysis、link analysis和citation indexes做為檢索的問句，同時再加上Scientometrics和Journal of Informetrics兩種期刊的論文，從Web of Science資料庫中進行檢索。結果共檢索出4404筆論文資料。

在這些論文資料裡，共有75個國家。以地區來區分，歐洲在每個時段上具有最大的貢獻，不論是數量或所占比率都有成長，亞洲所佔的相對比例在22年間有很大的成長，北美雖然在數量上有成長，可是相對的比例呈現緩慢的下降。每個地區的作者會偏好在本身地區的期刊上發表，舉例而言，歐洲作者發表論文的前五個期刊中有四個歐洲期刊，南美也有類似的情形，但是亞洲的情形例外，前五個期刊中有四個是歐洲期刊，另一個則是北美的期刊。

自1990年代中期後，國家間的合作情形增加許多，之前國際合作的論文每年為1到19篇，2008年已大幅增加為96篇。美國是國際合作佔最多的國家，但以地區來說，歐洲平均每個國家的國際合作數為5.78篇論文，多於世界其他部分的4.47篇論文。

此外，歐洲則有許多具有國際合作經驗的機構，共有16所研究機構有國際合作經驗，北美則有8所，亞洲有1所。機構間的合作來說，在1987年每篇論文平均只有1.1個機構，但在2007年則增加為1.96。

本研究且利用MDS、VOSviewer和Pajek將這些論文上的國家與機構之間的合作關係，呈現為圖形。

In metrics research, the United States also has the highest share of international collaborations, but the average number of collaborations with European countries was higher (5.78 publications per country) than for other parts of the world (4.47 publications per country).

This investigation was prompted by interest in whether shifts in productivity based on geography are observed in the bibliometrics, informetrics and scientometrics areas.

One of the authors conducted a pilot study to determine whether there have been clear declines in North American contributions to the metrics literature base (Wolfram, 2008). The author found that there was indeed a notable relative decline in North American contributions and a sharp increase in European contributions.

Hood and Wilson (2001) examined the growth of literature of the metrics area. They provided an historical treatment of the development of these areas that included earlier studies of the field. In their research, literature associated with bibliometrics, informetrics and scientometrics was compared for the period 1968–2000. The authors noted that bibliometrics was still the most widely used term for metrics research.

More recently, Stock and Weber(2006) conducted a Web of Science search for records specifically including metrics terms and allied areas. They observed contributions had grown substantially since 1980.

Search parameters included the Boolean ORed result of bibliometrics, scientometrics, informetrics, cybermetrics and webometrics, in truncated form (e.g., webometri*), along with the phrases “citation analysis”, “link analysis” and “citation indexes”. ... These search results were ORed with the two primary journals that publish metrics research that are indexed by WoS, namely Scientometrics and the Journal of Informetrics.

A pair-wise comparison of all collaborations at the national and institutional levels was then conducted from which a cooccurrence matrix could be compiled.

Multidimensional scaling (MDS) analysis was used to visualize the relationships among countries. Because the data represent a type of similarity measure represented as a symmetric matrix, SPSS PROXSCAL was used to construct the map, as recommended by Leydesdorff and Vaughan (2006).

The recently developed visualization tool VOSviewer (van Eck &Waltman, 2010) was also used to provide an alternate visualization of the relationship outcomes. Like MDS, VOSviewer (http://www.vosviewer.com/) relies on a distance-based approach to mapping informetric relationships. Instead of using more traditional similarity measures to produce a normalized outcome for co-occurrences as used in MDS, relationships are based on association strengths, so the algorithm is somewhat different than PROXSCAL and, therefore, can produce different outcomes. Details of the comparison of different measures can be found in van Eck and Waltman (2009).

The network visualization software Pajek (http://vlado.fmf.uni-lj.si/pub/networks/pajek/) was used as well. Unlike the distance-based mapping of PROXSCAL and VOSviewer, Pajek produces directed or undirected network maps, with the strength of the relationships represented by the thickness of connecting lines between vertices on the map. Distances are used more for clarification, but proximities do not necessarily indicate a stronger relationship.

The search parameters retrieved 4404 publications.

Europe shows the highest levels of contribution, both in absolute and relative terms over the time period of the study. Growth patterns in absolute terms are nonlinear based on trend line analysis in MS Excel; however, the R-squared goodness-of-fit values for even the best fitting models (higher order polynomials) were never more than 0.95, indicating a less than desirable fit.

Relative contributions based on geographic divisions have been largely stable. An exception is Asia, which had an increasing relative contribution over the 22-year time frame of the study. Although North American contributions have continued to increase in absolute numbers, the relative contribution shows a slow average decline over time.

The top five journals listed for each continent demonstrated a regional preference for publication outlets from that region. So, for example, four of the top five journals for European publications were published in Europe, and four of the top five journal outlets for South America were South American. The exception to this was Asia. Four of the top five journals for Asian publications were European and one was North American. This outcome may be a reflection of the data extraction method, the indexing practices of WoS, or a preference during the study time frame for Asian scholars to publish in Western journals.

Seventy-five countries were represented in the record set.

The number of metrics papers published annually that represent collaborations between two or more countries has increased greatly since the mid-1990s. Prior to this time, the number of internationally collaborative papers ranged from 1 to 19 papers annually. Over the last decade this number has increased to a high of 96 papers in 2008.

In metrics research, the United States also has the highest share of international collaborations, but the average number of collaborations with European countries was higher (5.78 publications per country) than for other parts of the world (4.47 publications per country).

Sixteen of the institutions on the list are European, eight are North American, and one is Asian. The United States has the largest number of institutions represented (five), followed by Belgium (four – note: one institution merged with another institution to form a new entity).

There has been steady growth in inter-institutional collaboration over the 22 years. The mean number of collaborative institutional partners within the dataset has steadily increased from a low mean of 1.1 institutions per publication in 1987 to a high of 1.96 institutions per publication in 2007.

Europe, and in particular Western Europe, clearly dominates in the production of metrics literature. The United States continues to be the largest singular contributor, but this appears to be changing. North American contributions as a whole continue to increase, but represent a smaller percentage of worldwide production. European contributions have grown tremendously, especially during the last 5 years of the study period. This same period is marked by impressive growth from Asia.

It should be noted that WoS increased its coverage in 2008 by including more regional journals. These inclusions possibly could contribute to the increase in Asian contributions, but the observed growth for Asia was already evident prior to any such additions.

International and inter-institutional collaborations do not necessarily reveal strong geographic affinities, although the multiple institutional affiliations by a number of scholars associated with Flemish institutions do contribute to the strengthening of regional ties. Undoubtedly, the growth of the Internet and increasing availability of other telecommunication technologies have made these collaborations less distance dependent.

Hou, H., Kretschmer, H., & Liu, Z. (2008). The structure of scientific collaboration networks in Scientometrics. Scientometrics, 75(2), 189-202.

Hou, H., Kretschmer, H., & Liu, Z. (2008). The structure of scientific collaboration networks in Scientometrics. Scientometrics, 75(2), 189-202.

本研究利用社會網絡分析、共現分析(co-occurrence analysis)、叢集分析和詞語的頻率分析等多種分析技術，從Scientometrics期刊1978到2004年發表的1927筆論文資料，探討科學家合作網絡的結構特性、整個網絡上的合作領域以及個別的合作網絡、合作網絡上的合作中心(collaborative  center)。

過去的研究裡，Schubert (2002) 和 Dutt, Garg, & Bali (2003)都是針對國家間合作的巨觀層次。Kretschmer (2004) 認為巨觀和中觀(meso)層次的分析無法足夠地反映個人之間的合作趨勢，因此呼籲應在微觀層次的分析投注更多努力。

1927筆論文資料裡，單一作者的論文共有1052筆，所以仍稍占多數。作者數大於3的論文僅占非單一作者論文的13.71% (120/875)，顯然研究Scientometrics的團隊規模都不大。發表3篇論文以及以上的高生產作者共計234人，其中有69.66%的作者曾發表與其他作者合作的論文。將這些作者間的合作關係表現成網絡，並利用Bibexcel對這個網絡上的節點進行叢集分析，共發現22個叢集。前兩個較大的叢集分別有15與14個科學家。網絡上最大的相連成分上共有15個叢集，共有合作經驗的高生產作者中的96位，占58.90%。合作網絡共有401條連結線，網絡密度為0.03，顯示Scientometrics領域的合作很鬆散。

對每一個節點計算它們的三種中心性，結果發現中心性和對應作者的生產力之間有很顯著的正相關，表示高生產力的作者同時也活躍在Scientometrics領域的合作網絡上。其中Glänzel的程度中心性最高，總共和其他18位作者有合作關係。

以詞語的頻率分析每個叢集的主題，最大的兩個叢集有類似的主題，但使用的研究方法略有不同。此外，研究主題為科學合作的四個叢集間幾乎沒有連結，同樣的情形也發生在研究科學與技術之間關係的四個叢集。

The structure of scientific collaboration networks in scientometrics is investigated at the level of individuals by using bibliographic data of all papers published in the international journal Scientometrics retrieved from the Science Citation Index (SCI) of the years 1978–2004.

Combined analysis of social network analysis (SNA), co-occurrence analysis, cluster analysis and frequency analysis of words is explored to reveal: (1) The microstructure of the collaboration network on scientists’ aspects of scientometrics; (2) The major collaborative fields of the whole network and of different collaborative sub-networks; (3) The collaborative center of the collaboration network in scientometrics.

Schubert [8] and Dutt etc. [9] presented international collaboration characteristics in the scientometrics community itself, focusing on country aspects at macro level.

Kretschmer [6] appealed to devote more efforts to investigations at micro level in the future because the knowledge at meso and macro level does not yet adequately reflect the trends in cooperation between individuals.

The study is based on bibliographic data retrieved from the Web of Science. The data contains all types of documents published in Scientometrics during 1978 to 2004.

In this study we have adapted an integrated procedure of social network analysis (SNA), co-occurrence analysis, cluster analysis and frequency analysis of title words.

Bibexcel is designed as a tool for manipulating bibliographic data, which is a free online-software published by Persson. In the present study, Bibexcel is used to do cooccurrence analysis and cluster analysis.

Following the methods of Otte & Rousseau [11], White [13] and Kretschmer & Aguillo [12], SNA was applied to display the microstructure of collaboration networks in scientometrics with Pajek.

Moreover, we used frequency analysis of title words to display the main collaborative field of different sub-networks. The software for frequency analysis is demo version of Wordsmith Tools published by Oxford University Press and available online.

There were 1927 documents published in Scientometrics during 1978 to 2004 (see Table 1).



From Table 1, we found that the pattern of co-authorship was still dominated by single-authored papers as the conclusion drawn by Dutt etc. [9].

While the number of multi-authored papers (the number of co-authors is more than 3) accounts for 13.71% only, which indicates that team size in scientometrics is not large.

In order to show the main structure of the network, each author must published 3 papers or more to be included in this integrated analysis. This threshold resulted in a total of 234 prolific authors publishing 3 or more papers during 1978 to 2004, among them there are 163 authors published co-authorship papers, accounting for 69.66% of the prolific authors.



Based on cluster analysis embedded in Bibexcel, we gained 22 clusters circled by solid lines (see Figure 1). We identified these clusters as sub-networks in the field of scientometrics.

The largest subnetwork is number 1 that has 15 collaborators, and the second largest one is number 2, which has 14 collaborators, and so on.

We noticed that there was totally 15 subnetworks connected with each other composing the largest central component, which had 96 numbers accounting for 58.90% of the prolific authors published co-authorship papers.

Density is an indicator for the general level of connectedness of the graph. ... In the present study, there are totally 401 links in the network, so the density of the network is 0.03, which indicates that the collaborative network in the field of scientometrics is very loose.

So an author who has high degree centrality must has collaborated with many other authors, which means the author is a central collaborator of the whole network. In the present study, Glänzel who has 18 co-workers is the central author of the whole network.

We found a positive and significant correlation between output of authors and the centrality measures (r=0.648, 0.437, 0.338 respectively at the 0.01 level, see Table 4) after investigating the correlations between output and the three centralities of the 125 authors in the 22 sub-networks, which indicated that most of the prolific authors are also active in collaboration network in the field of scientometrics.

We have also presented the main collaborative field of different sub-networks in scientometrics and found that the two biggest sub-networks have the similar collaborative topic with slightly methodological difference. In addition, we found an interesting phenomenon that four sub-networks dealing with scientific collaboration didn't collaborate with each other except sub-network 3 and 12. Moreover, four subnetworks studying technology and science never collaborated with each other at all.

Chen, Y. W., Fang, S., & Börner, K. (2011). Mapping the development of scientometrics: 2002–2008. Journal of Library Science in China, 3, 131-146.

Chen, Y. W., Fang, S., & Börner, K. (2011). Mapping the development of scientometrics: 2002–2008. Journal of Library Science in China, 3, 131-146.

本研究利用社會網絡分析與科學地圖映射(science mapping)分析Scientometrics期刊2002到2008年發表的816筆論文。

針對Scientometrics期刊進行書目計量分析的相關研究，包括：Schoepflin and Glanzel (2001)將Scientometrics在1980、1989和1997年發表的論文分別進行歸類，發現科學政策(science policy)和科學社會學(the sociology of science)的比率在下降。Peritz and Bar-Ilan (2002)發現Research Policy和Social Studies of Science分別是1990和2000年Scientometrics論文引用的期刊次數最多的第三名和第四名。Chen, McCain, White, and Lin (2002)分析出1981到2001年間Scientometrics期刊的引用及共被引模式。Hou, Kretschmer, and Liu (2008)對2002到2004年間Scientometrics期刊上的作者合作網絡的結構特性進行分析。Dutt, Garg, and Bali (2003) 則分析Scientometrics期刊1978到2001年間論文資料上的國家、機構在主題上的分布。

本研究在816筆論文資料上共計發現57個國家，具有較大生產力的國家主要是歐洲國家。前十個較大生產力的國家裡，美國、比利時、西班牙、中國和德國都有相當快速的年增率，但印度的年增率是負的。生產力較大的國家的被引用次數也比較高。

為了國家間的研究合作情形，本研究提出相對合作強度(relative collaborative intensity, RCI)，這個測量方式整合了合作的國家數和合作的次數兩種指標，其公式如(3)所示：

假設(RCI)_i是第i個國家的相對合作強度，其中CC_i和CT_i分別是這個國家合作的國家數和與其他國家合作的次數。在本研究裡，比利時是相對合作強度最高的國家，英國、荷蘭與美國則分居2到4名。

接下來將國家間的合作關係表現成網絡圖，圖形上最大的相連成分(connected component)共有37個國家。在這個相連成分上，比利時、英國和匈牙利之間都有很強的連結。

以機構來看，比利時的Katholieke Univ Leuven、匈牙利的Hungarian Academy Science和荷蘭的 Leiden Univ發表的論文數和被引用次數最多。

進一步分析前十個主要機構的被引用次數最多的前十筆論文資料，發現引用它們的論文主要來自圖書資訊學、電腦科學、資訊系統和跨領域應用(interdisciplinary applications)等領域。但台北醫學大學的一篇論文則被許多生物醫學領域的論文引用。

就論文的合作作者數來分析，本研究發現單一作者的論文有271篇，多位作者的論文有545篇，每篇論文平均有2.29位作者。Dutt, Garg, and Bali (2003) 研究1978-2001年間的論文，單一作者的論文占半數一上，平均合作作者數則為1.73。兩相比較之下，由多位作者的論文數和平均作者數增加的結果，能夠顯示Scientometrics期刊上的合作情形增多。

從引用的文獻分析Scientometrics的主題包括科學與技術的關係(the relationship between science and technology)、個人科學研究產出的量化指標(indexes to quantify an individual's scientific research output)、作者的合作現象(author collaborations)、共被引網絡(co-citation networks)、科學引響力以及國家富強(the scientific impact and wealth of nations)。

The purpose of this article is to use the methods of Social Network Analysis and Science Mapping to make an analysis on the 816 papers published in the international journal Scientometrics from 2002 to 2008.

The major tools used in this paper were TDA, NWB and Excel.

Börner (2006) discussed the mapping research on structure and evolution of science.

Börner, Penumarthy, Meiss, and Ke (2006) mapped the diffusion of information among 500 major U.S. research institutions based on the 20-year publication data set published in the Proceedings of the National Academy of Sciences (PNAS) in the years 1982-2001.

Boyack, Börner, and Klavans (2009) mapped the structure and evolution of chemistry research over a 30 year time frame based on Science (SCIE) and Social Science (SSCI).

Leydesdorff and Rafols (2009) made a global map of science based on the ISI subject categories.

For instance, Schoepflin and Glanzel (2001) found a decrease in the percentages of both the articles related to science policy and to the sociology of science by classifying the articles published in Scientometrics in the years 1980, 1989 and 1997.

Peritz and Bar-Ilan (2002) analyzed the papers published in Scientometrics in 1990 and 2000 and found that Research Policy and Social Studies of Science are the third and fourth most frequently referenced journals in articles published in Scientometrics.

Chen, McCain, White, and Lin (2002) drew upon citation and co-citation patterns derived from articles published in the journal Scientometrics (1981-2001).

Hou, Kretschmer, and Liu (2008) analyzed the structure of scientific collaboration networks in scientometrics at micro level (individuals) by using bibliographic data of all papers published in Scientometrics of the years 2002-2004.

Dutt, Garg, and Bali (2003) made an analysis of papers published by Scientometrics during 1978 to 2001 by scientometrics assessment on countries and themes distribution, comparison of institutions and co-authors.

The analysis of 816 papers published in Scientometrics during 2002-2008 showed that they were contributed by 57 countries (or regions). ... Most of the 57 countries were from Europe. Other major countries (or regions) had a larger number of papers were USA and Canada in North America, China, India, Taiwan, South Korea and Japan in Asia, Brasil in Latin America, and Australia.

Fig. 2 had clearly illustrated the average annual growth rates of TOP10 countries, from which we can conclude that USA, Belgium, Spain, China and Germany had higher growth rates and India had a negative growth rate.

From Fig. 3 we could see that all the TOP 10 countries had a higher number of times cited. It indicated that the papers contributed by those countries were of higher quality and had more impact.



In order to visualize the relative intensity of collaboration, this article introduced the concept of Relative Collaboration Intensity (RCI) indicator. The average number of collaboration countries (CC), average collaboration times (CT) and Relative Collaboration Intensity (RCI) of the 10 countries were given in formula (1), (2) and (3):



We found that Belgium had the highest relative collaboration intensity, and England, Netherlands and USA ranked 2, 3 and 4.

In order to make a clear vision about the collaborations among all the countries/regions (57), the country collaboration network had been made with the method of SNA by NWB. ... The largest connected component in the network had 37 nodes, and there is another small component with 2 nodes.

Fig. 4 showed the largest component with 37 countries, which depicted that Belgium, England and Hungary had formed an strong connection. The largest connection lied between Belgium and Hungary, and the collaboration times were 27. Fig. 4 also showed that although the USA had the largest number of papers, the collaboration activity was weaker than Belgium, Hungary, England and Finland. USA had paid much more attentions to collaborate with Canada, England and Australia. Netherlands had collaborated with many countries, however, the collaboration times were fewer compared to Belgium, England and Finland.

The data showed that Katholieke Univ Leuven (Belgium), Hungarian Academy Science (Hungary) and Leiden Univ (Netherland) ranked from first to third both in number of papers and times cited and all of them had a biggish advantage to others.

We select the Most-Cited paper (that had the highest value of times cited) of each TOP 10 TC/P institutions and get 10 Most-Cited papers finally. By analyzing their citing papers, we found that the citing papers which had cited the Most-Cited paper of each institution distributed mainly in the fields of information science & library science, computer science, information systems and interdisciplinary applications ....

So a conclusion could be made that although an institution did not have many papers or hold the advantage of research activities, it could carry out one or some significant works that had a great impact on the future development of information science & library science. And some research work on scientometrics had also affected the development of some other scientific fields, such as the work of Taipei Med Univ.

Another study carried out by Dutt et al. (2003) in scientometrics showed that the average number of authors per paper was 1.73 during the period of 1978-2001. We studied the average number of authors per paper published in Scientometrics 2002-2008 and found that the value was 2.29, which indicated that collaboration in scientometrics had been growing since 2001.

To analyze the intensity of co-authorship pattern, the whole data (816 papers) had been divided into two groups, which were single authored (271) and multi-authored (545). Compared to the result made by Dutt et al. (2003) that more than half of the papers were single authored, we found that the ratio of papers written by two or more authors had increased rapidly from 2002-2008.

Table 6 listed the TOP 10 authors according to their number of papers. Compared to Fig. 6 we could find that all the TOP 10 authors were appeared in the biggest collaboration cluster. It was interesting to note that the TOP 10 authors collaborated with each other either directly or indirectly.

Most of the TOP 20 cited references had distributed in big co-citation clusters shown in Fig. 7. ... All these four highly cited papers in the biggest cluster were focusing on the relationship between science and technology especially for the effect of science on technology. ... The second largest cluster contained 19 nodes, two of which were ranked in TOP 20. The topics were about indexes to quantify an individual's scientific research output (Hirsch, 2005). The third largest cluster included three nodes listed in TOP 20, whose topics were about author collaborations (Glanzel, 2001; Katz & Martin, 1997; Narin, Stevens, & Whitlow, 1991). There were another two clusters containing two TOP 20 nodes, and one had 10 nodes, whose topics were on co-citation networks (De Solla. Price, 1965;Small, 1973), the other had only two nodes published in Nature and Science individually with the topic of the scientific impact and wealth of nations (King, 2004; May, 1997).

The major topic were social network analysis (Wasserman & Faust, 1994), Matthew effect in science (Merton, 1968), author self-citation (Glanzel, Thijs, & Schlemmer, 2004), country research performance (Moed, 2002), evaluation indicators of publication and citation (Schubert & Braun, 1986) and the calculation of web impact factors (Ingwersen, 1998).