A new evolutional model for institutional field knowledge flow network

The data presented in this paper are derived from papers published in APS journals during 1993-2013, the time, PACS code, author address information and citation relationship between papers are processed, the name of the research institutions in the author address information is extracted in the original address information, and after manual processing of the non-standard English institution name and spelling errors, the addresses that still do not identify the name of the institution are each labelled as “other”, and on this basis, the number of papers submitted by each institution was counted.

After conducting the necessary data processing procedures, it was revealed that a substantial number of research institutions, totaling 10,623, were involved in the study. The results obtained from the analysis shed light on the publication patterns within these research institutions. In particular, it was observed that a significant proportion of these institutions had a limited output of scholarly papers. To be more specific, out of the total research institutions examined, as many as 4,138 institutions were found to have only published a solitary paper during the designated period. Similarly, a staggering number of 7,808 research institutions demonstrated a relatively modest publication record, with no more than ten papers to their name. In stark contrast, only a small fraction of the institutions under investigation exhibited a prolific publication history, surpassing the milestone of one thousand publications. Upon scrutinizing the data presented in Figure 1A, it becomes apparent that the number of publications emanating from the top 100 research institutions has experienced a noticeable decline, shrinking to a mere 603 articles. As a result, the cumulative probability distribution graph illustrated in Figure 1A exhibits a more pronounced growth trend for lower publication counts, gradually plateauing as the number of publications exceeds 13. This finding suggests that there exists a distinct disparity in publication output among research institutions, with a greater concentration of institutions contributing significantly fewer articles.

Figure 1.

The graphical representation provided in Figure 1B unveils an intriguing trailing pattern, suggesting a substantial variation in the publication output among the research institutions. The observed pattern is consistent with the power law distribution, which aligns with the Pareto principle (Harvey & Sotardi, 2018). This principle dictates that a minority of entities contribute to the majority of the output, thereby resulting in a large variability in the output levels of the remaining entities. Specifically, the Pareto principle suggests that only approximately 20% of the research institutions can be classified as significant contributors, with a vast publication record, while the remaining 80% are considered less important entities with a considerably smaller output. Consequently, to ensure the comprehensiveness of the data and focus on the crucial institutions with a high volume of publications, this paper treats the extracted organizational addresses in the following manner:

For institutions in the top 1,000 in terms of number of papers, the sum of their articles accounted for 79.91% of the total number of papers, which can be attributed to a large-scale institution and is labelled in the form of “city - institution”. For institutions ranked lower than 1,000 in terms of the number of issued papers, the number of individual papers is small and the total number of papers issued by several institutions can only be essentially the same as the number of papers issued by a single large-scale institution, which can be attributed to a small-scale institution and is therefore consolidated according to the provinces and cities to which it belongs and labelled in the form of “city – other”. A portion of the data is not available from the author’s institution also consolidated according to the provinces and cities. and labelled in the form of “Others-city”. This yields a total of 3,185 addresses listed in three different formats.

Figure 2.

The Physics and Astronomy Classification Scheme (PACS) codes categories the fields of modern physics, where the highest level PACS code divides modern physics into 10 major subfields 00, 10, 20, 30, 40, 50, 60, 70, 80, 90, for example PACS code “47.56.+r” belongs to field 40 (Electromagnetism, Optics, Classical Mechanics), from which the field corresponding to each paper can be obtained. After identifying the institution and field of each paper, the “ institution-field “ to which the paper belongs is obtained by permutation and combination. The flow of knowledge between institutional field occurs through the citation relationship between papers. This means that knowledge flows from the cited institutional field to the citing institutional field. For instance, in Figure 2, paper C cites papers A and B, which both belong to multiple institutions and fields. Specifically, this indicates that knowledge flows from the institutional fields of A and B to those of C. The knowledge flow is consistent across all institutional fields, with each institutional field having a flow of XCitngCited. XCitngCited=1Citingp×Citedp×Citingn×CitingI×CitedI

Citing_p represents the number of fields divided by PACS encoding of the citing papers, Citing_n represents the number of reference articles in the citing papers, Citing_I represents the number of institutions contained in the citing papers. Cited_p represents the number of fields divided by PACS encoding of the cited papers, Cited_I represents the number of institutions contained in the cited papers.

In this way, the knowledge flow network is constructed to represent the institutional field, consisting of 8,900 nodes that represent 8,900 institutional fields. Due to the large number of institutional fields, it is not feasible to display them all. Thus, a network diagram as shown in Figure 3 illustrating the flow of institutional field knowledge among the top 100 institutional fields with the highest number of publications in 2013 is provided for reference. Nodes in the network correspond to specific institutional field, and the direction is from the cited institutional field, to the citing institutional field, in other words, knowledge flows from the cited side to the citing side. The nodes can be classified as either source nodes or sink nodes, with source nodes indicating where knowledge is disseminated outward and sink nodes showing where knowledge is received. Edges indicate the flow of knowledge between the source and sink nodes, which represent the two institutional institutions, and the weights of the edges indicate the flow of knowledge. The node’s total output represents the total publications of the institutional field size, distinguished by the node’s size in the graph. Different colors represent different fields. The top 100 fields with the highest number of publications are mainly concentrated in the 70 fields, with some in the 00, 10, 20, 60, and 90 fields. The remaining fields have relatively few publications.

Figure 3.

When conducting a comparative and analytical examination of the evolution of institutional field and the knowledge transfer between them within the institutional field knowledge flow network over time, it becomes evident that the network’s evolutionary characteristics primarily manifest in the augmentation of both the quantity and selection of edges (knowledge transfer). In particular, Figure 4(A) illustrates the growth trends of nodes and edges, revealing fluctuations in the number of new joining nodes and inconsistent variations in the number of newly added edges per node. This dynamic nature implies that the size and complexity of the institutional field knowledge flow network undergo continuous transformations throughout its development. Furthermore, the expansion of the institutional field knowledge flow network can be attributed to two distinct methods. Firstly, newly added edges are created by leveraging pre-existing nodes as sources, facilitating the integration and dissemination of knowledge within the network. Secondly, new joining nodes, which originate from outside the existing network, act as source nodes, generating newly added edges and fostering network growth. These mechanisms contribute to the evolution and enrichment of the institutional field knowledge flow network. Figure 4(B) provides further insights into the establishment of newly added edges within the network, highlighting four discernible pathways through which this occurs:

A new edge is created between a pre-existing source node and other preexisting nodes. A novel edge is established between two pre-existing nodes that previously had no connection. Specifically, this connection indicates that new knowledge is still being exchanged between pre-existing institutional field, with continuous cross-collaboration and information sharing across institutional field.

Figure 4.

Moreover, it is imperative to highlight that, when adopting a meso-level perspective, a substantial portion of the network’s expansion occurs within the actual pre-existing nodes. This aspect often eludes the attention of many academic scholars, but it plays a pivotal role in elucidating the intricate dynamics and configuration of knowledge flow networks. By focusing on the interactions and connections between established nodes, we gain valuable insights into the continuous evolution and refinement of the network. These inter-nodal exchanges, although less conspicuous, contribute significantly to the overall growth and transformation of the knowledge flow network. Neglecting this aspect would lead to an incomplete understanding of the network’s development trajectory and its underlying mechanisms.

The evolutionary mechanism of the BA model and its extended version is based on the principle that new joining nodes tend to preferentially connect to pre-existing nodes with higher degrees. This results in earlier joined nodes having higher degrees and consequently making fewer connections to newer nodes. However, this mechanism diverges from the evolutionary characteristics exhibited by the institutional field knowledge flow network. It fails to account for factors such as the variable number of new joining nodes, the random nature of edge formation, and the utilization of pre-existing nodes as sources for generating newly added edges within the evolutionary process. In order to more accurately capture the evolution traits of the institutional field knowledge flow network, this study introduces an Institutional Field Knowledge Flow Network Evolution Model (IKM). This model enhances the preferential attachment and growth observed in scale-free BA networks, while incorporating three adjustment parameters to simulate the selection of connection targets and the types of nodes involved in the network evolution process. The IKM integrates various connection targets and their respective preferred connection probabilities into the connection strategy, providing a more nuanced approach to modeling the evolution of the institutional field knowledge flow network. By accounting for the diverse factors at play in the evolution process, this model aims to offer a more comprehensive and accurate representation of the network’s development and growth dynamics. The algorithmic flow is illustrated in Figure 5.

Figure 5.

Upon careful examination of the foregoing observation, it becomes evident that a notable disparity exists in the ranking of total publications between the actual and the simulated network. In contrast, the number of total citations and the PageRank value demonstrate a relatively favorable alignment. Consequently, in order to gain deeper insights into the variation in total publications between the simulated and actual networks, a detailed investigation is warranted. This entails conducting a comparative analysis of the total publications simulated by the BA and DMS models. By juxtaposing the distribution of total publications in the simulated network from these three models with that in the actual network, a comprehensive understanding of the underlying dynamics can be achieved. The outcomes of this comparison are visually presented in Figure 7, offering a clear representation of the findings for further scrutiny and interpretation.

Figure 7.

It becomes apparent that the distribution of total publications yields distinct patterns across the IKM, DMS, and BA models in comparison to the actual network. Notably, when the number of total publications is at a minimal value of 1, the IKM model demonstrates results that closely resemble those of the actual network, with the DMS model following closely behind. In contrast, the BA model exhibits the most significant deviation in terms of the frequency of total publications. Furthermore, within the range of 10-100 total publications, both the IKM and DMS models present nearly identical outcomes that closely approximate the actual network, while the BA model showcases a higher level of disparity. As the total number of publications surpasses 100, all three simulated networks exhibit alignment with the actual network, indicating convergence in this higher range.

It provides additional insights through the presentation of cumulative probability distributions under varying total publications. Here, the IKM model notably mirrors the characteristics of the actual network with remarkable accuracy. Conversely, the DMS model displays slightly less efficacy, while the simulated BA model’s network demonstrates a more pronounced deviation from the actual network. Through an evaluation of the frequency of total publication and the cumulative distribution probability of total publication, it becomes evident that the IKM model outperforms its counterparts, showcasing superior performance among the three models. This suggests that the IKM model excels in effectively simulating the actual network across varying total publication scenarios, thereby establishing its robustness and reliability. Conversely, the BA model demonstrates greater suitability for larger total publication scenarios. These findings underscore the IKM model’s capacity to enhance the BA model with growth and selection mechanisms, ultimately culminating in an improved model fit and heightened accuracy in representing real-world network dynamics.

In order to further investigate the relationship between the number of total publications in the simulated network and the actual network, this study seeks to assess the extent to which the distribution of total publications in the institutional field knowledge flow network aligns with that of the actual network. To accomplish this, a non-parametric statistical method known as the Two-sample KS test (Berger & Zhou, 2014) is employed to evaluate the similarity between two independent distributions. Specifically, the KS test is utilized to determine whether the quantity of total publications in the simulated network generated by the IKM, BA, and DMS models adheres to the same distribution as observed in the actual network. By subjecting the simulated and actual networks to this rigorous statistical analysis, a comprehensive understanding of the resemblance between their respective distributions can be obtained. The resulting data was compared in Table 1.

Based on the test findings, at a significance level of 0.05, the values of the BA and DMS models’ test outcomes are 2.972×10^-309 and 0.013, respectively. Both values are below 0.05, indicating that the number of total publications distribution in the network simulated by the BA and DMS models does not align with the actual network. Conversely, the IKM model outperforms them. At a significance level of 0.05, the value of the IKM model is 0.142, which exceeds the threshold. Therefore, the distribution of the number of total publications in the simulated network by the proposed IKM model aligns with that of the actual network and belongs to the same distribution. This provides further evidence that the IKM model can effectively elucidate the evolution of the institutional field knowledge flow network.

To gain further insights into the network dynamics, both the BA and DMS models were utilized to rank the nodes’ importance using PageRank. Additionally, a Pearson correlation test (Cohen et al., 2009) was conducted to examine the relationship between the number of total publications, the number of total citations, and the PageRank values in comparison to the actual network. Figure 8 illustrates the outcomes of these analyses.

Figure 8.

Over the years, the number of fields within the network steadily increased. Notably, when scrutinizing the correlation between the three simulations produced by the BA model and the actual network, a distinct downward trend becomes apparent. It is important to highlight that prior to 1995, the correlation of the BA model surpassed that of the IKM and DMS models, approaching a value close to 1. During the period spanning 1996 to 1998, the correlation between the IKM and DMS models exhibited similarity. However, from that point onwards, their correlation began to diverge. This observation suggests that the BA model is proficient in replicating a network structure that closely resembles the actual network during its initial stages. Nevertheless, as time progresses, the quality of the simulation deteriorates, leading to an increasing disparity between the model and the actual network. Consequently, the BA model’s ability to accurately capture the network dynamics diminishes, limiting its viability to shorter simulation durations. By conducting these comprehensive analyses, valuable insights are gained regarding the performance and limitations of the BA model in replicating real-world network behavior. These findings contribute to a deeper understanding of the complexities underlying network growth and provide crucial information for future model enhancements.

The correlation analysis reveals a strong positive relationship between the PageRank algorithm and the number of total citations in both the IKM and DMS models. This correlation demonstrates a consistent upward trend throughout the simulation period. Notably, in the IKM model, the correlation between the PageRank algorithm increased from 0.893 to 0.952. Similarly, in the DMS model, this correlation rose from 0.902 to 0.950. Moreover, when examining the correlation between the number of total citations in the IKM and DMS models, it increased from 0.840 to 0.939 and from 0.851 to 0.937, respectively.

The positive correlation between the PageRank algorithm and both the number of total publications and the number of total citations in the IKM and DMS models is noteworthy. However, there exists a notable disparity in the number of total publications generated by these models. The correlation between the number of total publications in the IKM model’s replicated network and the actual network consistently remains around 0.880. On the other hand, the correlation between the total number of publications in the DMS model’s network and the actual network gradually improves from an initial value of 0.801 to 0.878. Despite this improvement, the correlation in the DMS model remains slightly lower than that of the IKM model. These findings indicate that while the IKM model demonstrates superiority in terms of PageRank and total citations, it also holds a distinct advantage in replicating the total number of publications.

Additionally, the highest correlation coefficient obtained through the PageRank algorithm provides insights into the evolution mechanisms of knowledge flow networks. It suggests that nodes within the knowledge flow network that contribute more knowledge tend to acquire a greater number of connections as the network evolves. In summary, the IKM model exhibits significant advancements across various aspects when compared to the BA and DMS models, with its simulation effectiveness consistently improving over time.