Introduction

Knowledge evolution offers a unique and powerful road map for understanding knowledge creation, learning, and performance in everyday work (Allee, 2012). For researchers and policymakers, an accurate understanding of the state-of-the-art of a research field is needed to maintain scientific creativity.

Further, academic entities, such as authors, papers, and journals, are also carriers of knowledge. The keywords given by authors are concentrated summaries of documents. Author-selected keywords refer to the lists of keywords selected by author(s) to represent the content of the underlying scientific article (Uddin & Khan, 2016). Many studies have used keywords and their relationships to map the knowledge structure in a series of articles (Peset et al., 2020; Su & Lee, 2010). Co-occurrence, citation, and co-citation relationships link keywords provided in the literature to shape the knowledge structure (Choudhury & Uddin, 2016; Zhu et al., 2015). Literature keywords comprise an efficient corpus for shaping the scientific knowledge structure because of the informative relationships between keywords and because keywords provide understandable content to represent knowledge. Keyword co-occurrence networks constitute the basic structure of knowledge map analysis (Uddin et al., 2015).

However, the keyword relationship approach to shaping the knowledge evolutionary process considers only one kind of relationship at a time. Both temporal and sequential knowledge structures are considered to describe the long-term evolutionary process of knowledge. Moreover, scientific innovation and advancement have been based on combining existing knowledge (Uzzi et al., 2013; Wang et al., 2017). Scholars have argued that papers and patents are a combination of knowledge elements rather than elements of knowledge themselves (Lee et al., 2010; Su & Lee, 2010). As a trace of knowledge evolution, traditional keyword network analysis uses the keyword as a network node, and the network edge represents the co-occurrence and citation relationships. The evolutionary process of network edges has not been as thoroughly discussed as that of network nodes. Additionally, as the keyword providers, authors decide which keywords are chosen in their research and whether to continue their use in future papers (Lu et al., 2021). Single relationships of keywords lack information to explore the role of the same author in the knowledge evolutionary process.

Therefore, we analyze the knowledge evolution process within a research field using multiple relationships, including keyword pair-based citation relationships, the same author trace, and keyword co-occurrence relationships. Keyword co-occurrence pairs are divided by year and represent the temporal knowledge structure of the research field of informetrics. The indirect citation relationship consists of keyword co-occurrence pairs and citations for these keyword pairs. The keyword pair citation relationship represents the sequential trace of knowledge pair evolution, and the same author trace indicates keywords provided by the same author in different papers. The same author plays a vital role in the diffusion of knowledge, which could be traced using the keywords employed in their series of papers. In particular, we address the following research questions:

  • RQ1: How do the characteristics of the direct keyword co-occurrence pair depict the knowledge evolutionary process?

  • RQ2: What are the unique characteristics of knowledge evolution revealed by indirect keyword relationships based on the same author trace?

  • RQ3: What the keyword pair-based citation relationship explains for the knowledge evolutionary process?

Multiple relationships between keywords, citations, and same author trace were assessed to better understand the knowledge evolutionary pattern within a scientific field to answer these research questions. To this end, we first extracted keywords from papers related to informetrics research. Second, we constructed the direct keyword relationship paired with the keyword co-occurrence relationship and indirect keyword relationship paired with the edge-based citation and same author trace. Third, we investigated the characteristics of knowledge evolution revealed by the direct and indirect keyword relationships, and we discovered knowledge evolutionary patterns in the informetrics field over time.

The contribution of this paper is primarily to quantitatively measure the evolutionary process of knowledge within a discipline using multiple relationships. Both keyword co-occurrence and citation relationships are considered to shape the knowledge evolution structure. Additionally, five evolution stages are recognized within the research field of informetrics: knowledge generation, growth, obsolescence, transfer, and intergrowth. This work explains these evolutionary stages in detail and presents examples in the informetrics field. Moreover, the keywords provided by the same authors in different papers were labeled to trace the same author’s effect on promoting knowledge evolution.

Related work

Process stage of knowledge evolution

The previous scientific and technological knowledge trajectories imply that knowledge evolution is not random and follows a periodic life cycle (Dosi, 1982). Mina et al. (2007) mapped the medical knowledge evolutionary process and divided it into the emergence, growth, and transformation stages. In terms of the topic evolution model, the life-cycle events of a topic usually evolve by emerging, disappearing, merging, and splitting (Qian et al., 2020). With patent citation data, technological knowledge depreciation was identified (Liu, Grubler, et al., 2021; Liu, Yang, et al., 2021). Three general processes and two special processes are summarized in this research.

Knowledge generation

As is shown in Fig. 1. The edge < A, E > appears for the first time in a certain year in the evolutionary process. The new emerging edge < A, E > is used continuously for at least two years.

Fig. 1
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Schematic diagram of knowledge generation

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The generation of new scientific knowledge often occurs through the coming together, re-working, and re-formulating of previously distinct pieces of older knowledge and techniques into a new scientific synthesis (Hoch, 1985). The creation of new scientific knowledge builds on combining existing pieces of knowledge (Wang et al., 2017). Scholars have proved that novelty can be defined as unprecedentedly recombining pre-existing knowledge components (Arthur, 2009; Burt, 2004; Fleming, 2001). Therefore, the new knowledge generation reflected in the knowledge evolution within a discipline could be recognized with the new knowledge co-occurrence pair.

Knowledge growth

As is shown in Fig. 2. The weight of edge < D, F > keeps increasing in a certain period in the node-perspective evolutionary process.

Fig. 2
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Schematic diagram of knowledge growth

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Scientific revolution describes the next stage after knowledge generation as growth, which includes rapid and stable growth periods (Kuhn, 1962a, 1962b). Kuhn explains that the rapid growth period is the formation of a new scientific paradigm. When a new scientific paradigm encounters a new development bottleneck, the growth rate slows and enters a stable growth period. Earlier studies have attempted to mathematically assess the growth of knowledge as the consequence of knowledge diffusion (Modis, 2007). The growth of scientific knowledge is primarily due to the diffusion process of transmitting new ideas from person to person between scientific communities. The exponential increase in the literature is a good indicator of the knowledge growth processes (Chen & Hicks, 2004).

Knowledge obsolescence

As is shown in Fig. 3. The number of co-occurrence edges < D, F > becomes increasingly smaller in the evolutionary process.

Fig. 3
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Schematic diagram of knowledge obsolescence

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The term obsolescence was first proposed by Gosnell (1944) and meant becoming out of date or something that is increasingly less used. He pointed out that the obsolescence of information conceived by the literature is much slower than the literature itself. The obsolescence of literature was measured in two ways. The synchronic approach uses the publication timeline of the newer half of the total literature currently in use in a discipline (Burton & Kebler, 1960). The diachronic approach is to collect the annual citation count of the literature (Wang et al., 2019).

The underlying reason for obsolescence in literature is that the knowledge involved in the papers follows the knowledge evolutionary life cycle. When the knowledge in the research field has become dated or even wrong, the literature related to the dated knowledge is no longer cited. When the knowledge becomes part of the consensus of the scientific community, it continues to be in the knowledge graph every year but rarely receives many citations by future work. When knowledge is widespread in the scientific community, it is mentioned and cited with high frequency. However, many papers contribute to widespread knowledge, accelerating the obsolescence of earlier similar literature, corresponding to rapid scientific research activities in a discipline (Swanson, 1993). Obsolescence is proved to be reflected in the tendency of the citation rate of articles or patents to decay over time because of their reduced relevance for ongoing knowledge advancement (Higham et al., 2017). Knowledge obsolescence can be recognized when the knowledge no longer exists (is wrong) or is much less cited in successive years.

Knowledge transfer

As is shown in Fig. 4. The co-occurrence < D, F > in 2012 is cited by pair < A, E >, and the pair < A, E > continues to be cited in future years.

Fig. 4
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Schematic diagram of knowledge transfer

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Citations are the cornerstone of knowledge transfer in science. In addition, knowledge transfer refers to transfer in the process of both paper and patent citations (Abramo & D’Angelo, 2020; Hassan et al., 2018; Silvello, 2018). The transfer of knowledge is a condition of progress in human society (Loasby, 2002; Pu et al., 2021) because it offers a new use-value for aging knowledge. Qian et al. (2020) defined topic transfer as when the similarity between the two periods is greater than the predefined threshold value, and topic transfer is the underlying process behind knowledge transition.

Knowledge intergrowth

As is shown in Fig. 5. The edge < D, F > was strengthened with the growth of edge < A, E > in the node-perspective evolutionary process. In addition, there is a citation link between edge < D, F > and edge < A, E > in the edge-perspective evolutionary process.

Fig. 5
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Schematic diagram of knowledge transfer

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The intergrowth status of knowledge comes from the definition of the symbiosis theory in biology. Biology describes symbiosis as an organism participating in a symbiotic relationship in which two species derives a benefit from each other. However, the co-existence condition of knowledge in scientific activities is not as rigid as biological symbiosis; thus, the symbiosis relationship is not a unique relationship between knowledge to support continued knowledge growth. Scholars have called it knowledge co-existence (Réale et al., 2020; Urbano & Ardanuy, 2020) or knowledge intergrowth (Shi & Wang, 2009). This paper employs the term intergrowth, considering that scientific behavior should represent the benefit attachment relationship between the co-existing knowledge. Citations between literature provide a good way to depict the process in which one knowledge unit derives a benefit from another. The synchronized growth of these two co-existing knowledge units depicts the process in which the other knowledge unit is still active in the current scientific domain.

Content-based approaches to shape the knowledge evolutionary process

Scientific entities provide many approaches to trace knowledge evolution. Journals, articles, and authors act as knowledge carriers. The knowledge diffusion path could be identified through a network with the above entities as nodes (Börner et al., 2004). As with natural language processing technology, topics and keywords can be extracted efficiently and provide a more accessible knowledge representation than knowledge carriers. Topics and keywords, clustering algorithms, and network analyses have recently garnered considerable attention in identifying the knowledge structure and tracking academic knowledge evolution.

Topic modeling

Topic modeling methods aim to extract semantic topics from unstructured documents. Topic evolution is one branch that seeks to analyze how temporal topics in a set of documents evolve and has successfully identified content transitions (Jung & Yoon, 2020). Named entities or distinctive phrases could act as topic terms (b; Xu, Ding, et al., 2019). The last 20 years have witnessed a rise in the number of studies using topic modeling in numerous articles (Figuerola et al., 2017). The latent Dirichlet allocation (Blei et al., 2003) has been the most discussed among these. The knowledge evolution reflected by topic evolution requires field knowledge interpretation because topic modeling generates the probability distribution of a group of words that is not interpretable without human knowledge (Chang et al., 2009). Further, the topic evolution traced with citation path and co-occurrence relation tends to provide persistent terms, which could be regarded as the scientific meme or gene (Kuhn et al., 2014).

Additionally, the Dirichlet multinomial regression (DMR) model (Mimno & McCallum, 2012), where the publication date is set as the observed feature, was applied to analyze the distribution of the top 10 topics from 1978 to 2020 in informetrics. The evolutionary topic process reflected by topic modeling is at a more macro level than the evolutionary knowledge process because the topic association defined in the topic evolutionary process is always based on the similarity and dissimilarity between topics in several different time windows (Xu, Ding, et al., 2019; Xu, Zhang, et al., 2019). Even topic modeling could be combined with citation relationships to identify the topic evolution path. Knowledge depicted in the topic evolutionary process is in the form of conceptual clustering. When and what kind of knowledge innovation is generated in the evolutionary process is ambiguous. Topic modeling is good at tracking the flow of innovation and knowledge rather than describing knowledge structure (Kim et al., 2018).

Keywords analysis

The descriptor keywords for an article are usually abstract definitions of the research context focus of the article (Su & Lee, 2010). In bibliometric research, keyword analysis of publications provides an effective way to investigate the knowledge structure of research domains and explore the developing trends within domains (Hu et al., 2018). Scientific literature is often fragmented, implying that certain scientific questions can only be answered by combining information from various articles. In this way, knowledge in a given paper is represented by series of keyword pairs (van der Eijk et al., 2004). Keyword networks formed from published academic articles were analyzed to examine how keywords are associated and identify important keywords and their changes over time.

Keyword co-occurrence pairs are employed to discern relationships among various scientific concepts in scientific papers to reveal the temporal structure of scientific knowledge (Choudhury & Uddin, 2016; Khasseh et al., 2017; Sedighi, 2016). Keyword co-occurrence pairs have a direct relationship extracted from citing papers. The co-occurrence edge could be combined with keyword frequency weights, occurrence time, and semantic distance to emphasize the critical relationships between keywords. The keyword co-occurrence network is best suited to understanding the current topic knowledge (Lee et al., 2017).

Citation analysis symbolizes the transfer of scientific knowledge (Choi, 1988) and is prominent in scientific knowledge discovery (Lee et al., 2015). Keyword citation pairs have an indirect relationship, requiring at least two papers to provide a citation link from the citing and cited papers. Cheng et al. (2020) demonstrated that the keyword citation network could detect indirect connections between keywords, understand critical knowledge units, and find significant topics. New keyword connections that have not appeared in the existing co-keyword analysis can be captured. Garfield (1965) claimed that citing between literature indicates a topical association between two papers. The relationship between keywords in the cited and citing papers is also similar (Hu & Zhang, 2015; Khasseh et al., 2017). A high semantic similarity exists between the keywords of the two papers in the citation relationship.

The indirect keyword relationship could be associated with a co-citation paper and the same author. The keyword co-citation network is proposed to measure the keyword similarity in terms of the topological network structure. The indirect keyword relationship paired by the same author in a different paper is less discussed in previous research. The research on author name disambiguation has confirmed that two articles with the same author published in a short time interval have high topic similarity and knowledge similarity (D’Angelo & van Eck, 2020). Therefore, keywords within these two same author papers are more likely to be reusable. The keywords of previous and subsequent papers written by the same author include reused keywords and new emerging keywords. The reused keyword represents the follow-up study of a certain topic. The new emerging keywords form an indirect pair of keywords, indicating the evolution of the author (Lu et al., 2020). The small processes of individual knowledge evolution combined constitute the entire process of knowledge evolution in scientific communities.

Keyword pair-based citation relationships

A paper generally refers to and cites multiple references and may be cited by others, thus reflecting the inheritance and variability of scientific development (b; Liu, Grubler, et al., 2021). Previous studies have used papers, authors, and keywords as the nodes for the citation network to predict paper citations, assess scholar influence, identify the research front, trace the knowledge diffusion path, and so on (Abrishami & Aliakbary, 2019; Kim et al., 2018; Muñoz-Écija et al., 2019). The knowledge evolutionary process has emphasized that novel ideas are spurred by the original combination of different existing knowledge (Mukherjee et al., 2017; Uzzi et al., 2013). The advancement of knowledge depends on the novelty and quality of an idea and whether the idea attracts researchers’ attention (i.e., diffusion) and their research builds on it (i.e., adoption as a citation) (Furman & Stern, 2011; Liang et al., 2019; Parolo et al., 2015).

The process ignores the characteristic of the keyword combination pair using single keyword phrases as the node of a citation network. In a keyword-based knowledge graph, nodes are noun phrases of keywords that could represent knowledge concepts, whereas the edges between knowledge concepts illustrate a triple form of knowledge unit. Edge features contain essential information about graphs. In the traditional node-perspective network, the weight of the edge is calculated with the strength of two nodes, and the weight belongs to the first-order proximity between two nodes. The edge-perspective network involves the link and the related nodes and enables capturing higher-order structures in a graph (Zhao et al., 2018).

A study exists on a patent citation network and technology convergence of the patent pairs, where edge outliers are assumed to be the opportunity for innovation emerging (Zhang et al., 2017). In biomedicine, gene expression, drug treatment, and virus infection evolve in a stochastic and temporal fashion (Wu & Wu, 2013). The edge-network analysis, where a node represents a pair of connecting nodes (i.e., an edge in the traditional node network), has been proved effective to predict the predisease state (the state of an individual before the appearance of clinical symptom) and thus achieves early disease diagnosis (Yu et al., 2014). The edge network transforms the ‘node expression’ data in the node space into ‘edge expression’ data, making it possible to explore the edge space (i.e., correlation space) to classify a single sample (Zeng et al., 2014).

Proposed approach

Research overview

The study was designed to mine the knowledge evolutionary process through a direct keyword relationship paired within a citing paper, an indirect keyword relationship paired by the same author trace in a different paper, and an indirect keyword citation relationship formed by the keyword co-occurrence edge, as illustrated in Fig. 6. In the results, we divided the above knowledge pairs by year and analyzed the evolutionary process, including knowledge generation, growth, obsolescence, migration, and intergrowth.

Fig. 6
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Study structure

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Data collection

The field of informetrics is a broad term comprising all metrics studies related to information science, including bibliometrics (bibliographies, libraries, etc.), scientometrics (science policy, citation analysis, research evaluation, etc.), webometrics (metrics of the web, Internet, or other social networks, such as citation or collaboration networks), and so on (Egghe, 2005). Informetrics was selected for this study as the discipline case because it is fast-developing (Bar-Ilan, 2008) and highly interdisciplinary and is affected by the incessant evolution of information technology (Prebor, 2010). The authors working on this study have focused on informetrics research for many years and are familiar with the knowledge of informetrics.

Papers and the bibliographic information were collected from Scopus because it includes a more expanded spectrum of journals than PubMed and Web of Science (Klavans & Boyack, 2009; Leydesdorff et al., 2016) to collect papers on informetrics research with as much detail as possible. First, all papers published in the Journal of Informetrics or Scientometrics were selected because they are well-known international journals focusing on quantitative features and characteristics of science and scientific research. Afterward, we refer to Bar-Ilan’s (2008) retrieval strategy when she conducted a detailed review of the status quo of informetrics in the twenty-first century. High-frequency keywords from informetrics or scientometrics were extracted and used to improve the retrieval strategy. In the same way, papers related to informetrics that were published in other journals were collected from Scopus.

Only English journal articles were considered. After cleaning the irrelevant records, 8732 papers were related to the field of informetrics. Additionally, the bibliographic information of the references of these 8732 papers was also collected to provide a direct citation relationship between keywords. The references consist of papers published in non-library and information science journals. Collected reference papers with at least three citation relationships were considered to build the direct citation relationship to capture the stable and convincing knowledge evolutionary process of informetrics (Waltman, 2016). The retrieval strategy and dataset description are presented in Table 1.

Table 1 Retrieval strategy and description of the dataset
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The missing keyword rate is high in the collected dataset; thus, we extracted the keyword from the paper title (Xie et al., 2021). The counts of co-occurrence pairs, citation pairs, and the same author pairs are listed in Table 2.

Table 2 Pair counts of the datasets of the paper collection
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Multirelationship construction of the knowledge evolution process

Figure 7 shows the data preprocessing process for multirelationship construction between keywords. The raw data collected from Scopus are parsed into bibliographic information and then keyword are extracted. Based on the bibliographic information and keywords, three multirelationships are constructed. The multirelationship of the knowledge evolutionary process involves direct and indirect keyword relationships. The former refers to the keyword co-occurrence relationship, and the latter refers to the keyword co-occurrence edge’s citation relationship and the keyword provided by the same author but not within the same paper.

Fig. 7
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Data preprocessing process

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Direct keyword relation construction

As Fig. 8 illustrates, < A, C >, < B, C >, < B, E >, < A, D >, and < D, F > are co-occurrence keyword pairs. The co-occurrence relationship has no direction, meaning the pairs < A, B > and < B, A > are the same. These pairs are divided into different time slices according to the publication date of the respective papers. The links between two keywords are the annual co-occurrence frequency of the keyword pairs. The bold blue line indicates an increase in the frequency of co-occurrence in a given year. The blue line of disappearance indicates the disappearance of the co-occurrence in a given year.***

Fig. 8
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Direct keyword relationships

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Indirect keyword citation relationship construction

As Fig. 9 notes, < A, C >, < B, E >, < A, D >, and < D, F > are co-occurrence keyword pairs. The paper citation path from the citing to cited paper indicates the citation relationship from < A, C > to < A, D >, < A, D > to < A, D >, and < B, E > to < D, F > . Then, the indirect keyword citation relationship involves the link between these pairs above, as marked with the dashed red line. The pair-to-pair relationship represents the knowledge evolution path.

Fig. 9
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Indirect keyword citation relationships

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Indirect keyword relationship construction

The same author publishing two papers provides two groups of keywords, and the indirect keyword relationship is from the above academic process. As Fig. 10 presents, the edge of two keywords is the number of the same authors to whom those keywords belong, and we did not count the keywords listed in the same paper.

Fig. 10
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Indirect keyword relationships (the same author trace)

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Results

Knowledge evolutionary process based on direct keyword co-occurrence pairs

The keyword co-occurrence pairs are grouped by year. Hence, the year of the first occurrence is identified. The evolutionary increment of the direct keyword co-occurrence pairs is calculated using the keyword co-occurrence frequency of one pair at the current year minus the keyword co-occurrence frequency of the same pair during the last year. The evolutionary increment represents the annual change in one keyword co-occurrence pair. When the increment is greater than zero, the keyword co-occurrence pair indicates the temporary knowledge growth stage in the evolutionary process. In contrast, when the increment is negative, the corresponding pair indicates the temporary knowledge obsolescence stage in the evolutionary process. Thus, the evolutionary process has had rises and falls since its first emergence in the research field.

Table 3 presents the pairs of keyword co-occurrences that fluctuated the most during the evolutionary process. Columns 2 and 6 list the generation year of the keyword pairs. The growth and obsolescence years represent the year combination list in the incremental calculation of the evolutionary process. The year combination is written as the two years joined by an underscore. These keyword pairs in Table 3 might contain more than one set of year combinations.

Table 3 Knowledge evolutionary process based on direct keyword co-occurrence relationships
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Figure 11 presents the visualized evolutionary flow of these keyword pairs from Table 3. The starting point for each keyword pair evolutionary diagram is on the far right, corresponding to the generation year in Table 3. From right to left, the path in the Sankey diagram represents a fragment of the evolutionary process between two years. Then, the number beside the year is the current frequency of co-occurrence. The node height depends on the frequency of the keyword co-occurrence. If the node on the right is taller than the node on the left, the keyword pair experiences an obsolescence stage between two years. In addition, the reverse exhibits a growth stage between two years for this keyword pair.

Fig. 11
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Knowledge evolution flow based on direct keyword co-occurrence relationships

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The pairs of keyword co-occurrences that fluctuate the most during the evolutionary process have a long history in the research field of informetrics. The keyword pair of journal rank and journal impact factor emerged in 1984 and experienced three growth stages after its generation (Pair 7). However, it has experienced two transitory obsolescence stages in recent years. As the basic knowledge elements for bibliometric research, citation and citation analysis have two pairs (1 and 8). The results reveal that Pairs 1 and 8 have the most growth stage fragments, indicating that the bibliometrics- and citation-related knowledge pairs are permanently influential. Additionally, Pair 11 indicates research on scientometrics and gender issues, and Pair 12 indicates research on bibliometrics and altmetrics issues. Pair 11 and 12 are recent hot topics in the research field of informetrics, and the number of their growth stage fragments is less than for traditional informetrics knowledge, like Pair 9 (citation analysis and h-index) and Pair 5 (h‑index and bibliometric). Regarding research evaluation, as a well-known application area of scientometrics, the evolutionary process of Pair 6 indicates the continuous and prosperous growth of the knowledge combination in the field of informetrics.

Knowledge evolutionary process based on the indirect keyword relationship

The indirect keyword relationship is based on the same author trace whose relationships were constructed using the keyword as the knowledge pair element, and the two selected keywords were provided by the same author but in a different paper. Previous work has proved that articles by the same author share similar knowledge or ideas (Koppel & Winter, 2014; Mihaljević & Santamaría, 2021). In this way, the keyword pair represents that the author contributes to a short fragment of knowledge evolution.

Table 4 lists 10 representative indirect keyword pairs with the most same authors, including five indirect keyword pairs with the most same authors for the generation stage and five for the growth stage. Columns 3, 5, and 7 list the year of generation, growth stage, and obsolescence, respectively. Column 4 lists the same authors’ ScopusID for generation status, and Column 6 is for the growth stage. The number in parentheses is the number of the same authors. The year of obsolescence stage is listed without the same author trace because the obsolescence stage of the indirect keyword pair is not necessarily the result of the same author trace. Then, Fig. 12 presents a detailed evolutionary flow of each indirect keyword relationship paired by the same author trace. The direction of the evolutionary flow is from right to left, which is the same as in the Sankey diagram principle in Fig. 11.

Table 4 Knowledge evolutionary process based on indirect keyword relationships paired by the same author trace
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Fig. 12
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Knowledge evolution flow based on indirect keyword relationships paired by the same author

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Table 4 and Fig. 12 indicate that most pairs share different same author traces at different stages of evolution, suggesting that some authors have derived new combinations of knowledge elements, and some other groups of authors have followed these pioneers. Pairs 1, 3, 4, 5, and 7 have experienced more growth in recent years than obsolescence, and fewer researchers have contributed to the indirect keyword pairs than at the beginning. Pairs 2, 6, 8, 9, and 10 show different evolutionary patterns with Pair 1, where Pair 2 experienced more obsolescence than growth. However, more researchers have contributed to the indirect keyword pairs than at the beginning. Additionally, the evolutionary flow in Fig. 12 is sparser than in Fig. 11, which indicates that the scale of knowledge evolution based on the indirect keyword relationship with the same author trace is smaller than that identified by direct keyword co-occurrence relationships.

Knowledge evolution based on indirect keyword pair-based citation relationships

In relationships based on keyword pairs and citations, keyword pairs in the same papers were treated as nodes, and the edge denotes the paper citation relationship. Tables 5 and 6 reveal citing keyword pairs, cited keyword pairs, and citation years, demonstrating a citation relationship from the cited keyword pair to the citing keyword pair in the year.

Table 5 Keyword pairs conforming to the knowledge intergrowth process
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Table 6 Keyword pairs conforming to the knowledge transfer process
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Table 5 displays the keyword pairs eligible for the knowledge intergrowth process, indicating that these cited and citing keyword pairs experience a temporal growth stage as long as the citation relationship appears. The knowledge pairs represented by crown indicator and normal and by citation and normal is a case of intergrowth process, indicating to the researchers that the normalization of citation-related indicators is becoming more discussed in informetrics. Moreover, the intergrowth process between the knowledge pair represented by bibliometric and scientific collaboration and by coauthorship network and scientific collaboration indicates that research about scientific collaboration is becoming more popular. Further, web of knowledge turns out to be an important tool for informetrics research.

Table 6 presents the keyword pairs eligible for the knowledge transfer process. The cited keyword pairs experience a temporal obsolescence stage as long as the citation relationship appears. The knowledge pairs represented by bibliometric and h-index and by p-index and bibliometric are a case of the transfer process, demonstrating a slight temporal reduction in the research focus on the h-index replaced with the p-index.

Dirichlet multinomial regression topic trend

In this section, we set the publication date as the observed feature of the documents of the DMR topic model, which has a log-linear prior on the document-topic distribution function of the observed features of the document. Further, the DMR was applied by analyzing the distribution of the top ten topics from 1978 to 2020. The topic distribution for DMR topic modeling is presented. Figure 13 depicts the relative proportion of these 10 topic clusters. Table 7 lists the word in each topic cluster. The results of the DMR only describe the growth or obsolescence trend. The trends of the top 10 topics have increasing, consistent, or decreasing patterns.

Fig. 13
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Topic distribution (Dirichlet multinomial regression topic model)

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Table 7 Top ten words for each topic
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Table 8 shows the change of topic terms of five topics since 2016–2020. The five topic clusters are generated from each year's keyword information. It can be seen that topic terms in each cluster change over time. The term that scientific collaboration appears in the topic cluster #0 with terms “bibliometrics, citations, interdisciplinarity, and economics” in 2016 and then moved to the topic cluster #1 with terms “bibliometrics, altmetrics, scientometrics, and web of science” in 2017. After that, the term scientific collaboration transferred into topic cluster#1 in 2018, topic cluster #1 in 2019, and topic cluster #4 in 2020. However, how the relationship changes between the term scientific collaboration and others remain unknown.

Table 8 Top five topic clusters from 2016 to 2020
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Compared with the topic evolutionary process of DMR topic modeling, the knowledge evolutionary process shaped using keyword pairs and multiple relationships could describe a more fine-grained evolutionary process. The knowledge components are represented by keyword pairs, which is comprehensible. The changes in the number of keyword pairs could be measured by the smallest time interval because a small number of new papers is enough to cause a change in the number of keyword pairs. Topic words involved in each topic cluster are numerous and highly overlapped. The overlap is high because the scope of informetrics is not large, and research paradigms have not undergone many dramatic changes. Due to a large and highly overlapping distribution of topic words, changes in the topics require the participation of more papers and takes more time to accumulate.

Discussion

In this research, three relationships represent knowledge evolution: direct keyword relationships paired with keyword co-occurrence pairs, indirect keyword relationships paired with the same author trace, and indirect keyword citation relationships paired with the citation relationship. The former two offer insight into the knowledge evolutionary process with the annual change in the quantity of the same keyword pairs. The latter provides more information about how different keyword pairs interact during the knowledge evolutionary process.

First, a direct keyword relationship was constructed with keyword co-occurrence pairs to depict the knowledge components. The knowledge evolutionary process can be measured by the annual changes in the number of keyword co-occurrence pairs (Kim et al., 2021). The results demonstrate that annual increments in the quantity of keyword co-occurrence pairs can demonstrate three evolutionary stages: new generation, growth, and obsolescence. At least one growth stage is required for effective generation identification to ensure the meaningful new generation of knowledge pairs. A nonnegative increment represents a fragment of the growth stage, and a positive increment represents a fragment of the obsolescence stage. In this way, the fragmentary knowledge evolutionary process was measured in the pair view in informetrics. Moreover, the year is an effective evolutionary interval. Such an evolutionary fragment can shorten the interval to months or weeks for rapidly changing knowledge domains.

Second, papers completed by the same author in a similar period have higher knowledge similarity. The indirect keywords relationship based on the same author trace determines keyword pairs provided by the same author in a different paper. Changes in researchers can be identified in the same knowledge evolutionary process. The results reveal that in the evolutionary process of most knowledge pairs, the authors who promote them are not those who first proposed them.

Finally, the keyword pair-based citation relationship provides a citation-based trace for knowledge evolution because the citation trace has been proved to be available for knowledge diffusion measurement (Yu et al., 2010). Keyword pair-based citation relationships reveal how keyword co-occurrence pairs interact with each other during the evolutionary process. According to the keyword pair-based citation relationship, two evolutionary statuses exist: knowledge pair transfer and intergrowth. Knowledge pair transfer represents a knowledge flow from a cited to citing keyword pair, and the cited pair experiences segmental obsolescence as the citation relationship disappears. Tracing the continuous knowledge transfer process is beneficial to identify the frontier knowledge and ensure research innovation. Knowledge pair intergrowth indicates that cited and citing keyword pairs all experienced segmental growth stage along with the citation relationship appears. Intergrowth borrows from biology and refers to a mutually beneficial evolutionary connection between two sets of knowledge over a period. Identifying knowledge intergrowth pairs helps determine potentially influential combinations of scientific knowledge. References can be considered as knowledge providers (Wu et al., 2017), the citing papers are knowledge recipients. The citation network between citing papers and references has been applied to trace the diffusion process of scientific knowledge, which contains the knowledge meme. A knowledge meme is a text unit in scientific publications, which is distributed in many citing publications without being broken apart or altered (Kuhn et al., 2014; Mao et al., 2020). In this way, the citation relationship from the cited keyword pair to the citing keyword pair indicate a hereditary of combination of knowledge gene. Kuhn's the structure of scientific revolution (1962a, 1962b) explained that science is an episodic model where periods of conceptual continuity are interrupted by periods of revolutionary science. Therefore, the keyword combination pair is dynamic and ever-changing over time. The continuous knowledge combination has become an important meme supporting the development of the present knowledge domain. For sociological perspective, citing relations may infer networks of diffusion and influence (Gomez-Rodriguez et al., 2012). Link the social survey keyword pair from different time series, can clarify the relationship between things, and propose the possible social processes plan to achieve the most beneficial social outcomes. In addition, tracking the events provided a coherent representation of the news cycle (Dou et al., 2012). For political sides, tracking the information epidemics in the social media identified the political discussions community (Guerrero-Solé, 2017), and the political polarization on Twitter (Conover et al., 2011).

Conclusions

A single keyword using the frequency of a continuous period has difficulty exhibiting the structure of knowledge evolution. Thus, in this work, the direct co-occurrence relationship, indirect relationship by keyword pair citation relationship, and same author trace were analyzed, which could mine the evolutionary process quantitatively from a different perspective.

In the results, an empirical study of the informetric field was analyzed. The five evolutionary process stages include knowledge generation, growth, obsolescence, transfer, and intergrowth. Further, a DMR-based topic trend was compared with those results. First, knowledge evolution is a process of rises and falls, not a continuously smooth state. The life cycle of knowledge is longer than the research topic, and old knowledge can be renewed in recent years. The keyword co-occurrence pair (Table 3) of journal rank and journal impact factor emerged in 1984 and experienced three growth stages after its generation (Pair 7).

Second, prolocutors and promoters of knowledge are not the same scholars during the evolutionary process shaped by keyword pairs. Table 5 and Fig. 12 demonstrate that most pairs share different same author traces at different stages of knowledge evolution, suggesting that some authors generated new combinations of knowledge elements and that other authors followed these pioneers.

Third, citations trace the knowledge diffusion path and provide insight into how different knowledge pairs interact. In relationships based on keyword pairs and citations, the pairs (crown indicator and normal) and (citation and normal) and the pairs (bibliometric and scientific collaboration) and (coauthorship network and scientific collaboration) are two typical sets of intergrowth keyword pairs. Compared with relationships based on keyword pairs and citations, the DMR topic trend has difficulty mining the knowledge transform term at the micro-level, especially in the migration and intergrowth processes.

The main limitation of this study is that we only used informetrics papers and related reference papers. Future research should focus on verifying the applicability of the datasets for multiple disciplines.