Scientific problem-solving relies on efective organizational patterns of research collaboration. To recognize the more complex crosscommunity collaboration patterns of researchers in modern science, this study probes the central core structure of co-authorship networks at the mesoscale, aiming at understanding the emerging structural characteristics and functional performance of the efectiveness of complex research and innovation systems. Taking the field of physics as an example, combining the deep reinforcement learning pretraining model with the hub role information of the complex network, this study identifies both the provincial hub and global connector hub and the emergence of multi-core structures at the mesoscopic level of the scientific collaboration network. The existence of the multi-core structure reflects the spontaneous formation of "local centrality and global decentrality" in the scientific collaboration system, which makes the knowledge creation system economical at the structural level and eficient in the functions of global collaboration and knowledge difusion. Through an analysis of the structural and functional characteristics and mesoscale collaborative organizational structures of researchers, this study enhances comprehension and insights into the inherent factors propelling scientific development and the dynamics of collective knowledge creation. The findings contribute valuable perspectives for the establishment of inclusive scientific research management policies, fostering a more sophisticated scientific research and innovation system.
The scientific research and innovation system embodies a
form of "collective intelligence," where individual scholars
possessing specialized knowledge and intellectual
capacity collaboratively tackle intricate real-world challenges
through self-organizing coordination, thereby propelling
the advancement of knowledge domains [
Existing studies has demonstrated that co-authorship
networks typically exhibit typical heterogeneity, confirming
that these networks feature a high degree of uneven
distribution in connectivity [
Despite this, the investigation into the diversity of pivotal actors within expansive scientific collaboration networks remains underexplored, particularly concerning the identiifcation of mesoscale core structures that bolster global eficiency within large-scale social systems. There is a dearth of research addressing how researchers with varying levels of social capital or difering types of social linkages contribute to the social division of cognitive labor in scientific communities.
This study aims to address these pressing issues by
identifying and examining multi-core structures within
coauthorship networks using a mesoscopic lens that taps into
the inherent community structure. Leveraging a pre-trained
reinforcement learning algorithm[
This study focuses on the field of physics. We use the
scientific publications in the journals of the American Physical
Society (APS) from the period 1985 to 2009 [
In this study, we propose an interpretable framework to detect and analyze crucial core structures within large-scale co-authorship networks, integrating previously mentioned research concepts alongside club structure detection algorithms. This approach involves applying a second-stage "key player" detection algorithm, which ranks nodes in the co-authorship network based on their "criticality."
As depicted in Figure 1a-c, the network resilience experiment shows the significance of the key members detected using the deep reinforcement learning algorithm. Figure 1a illustrates the ratio of the maximum connected subgraph size to the potential maximum size after systematically removing nodes according to their ranked criticality. The sheer size and complexity of the entire co-authorship network make visualizing it challenging. Therefore, Figures 1bc present embeddings of the co-authorship network graphs between select communities (7, 10, and 14) to exemplify the influence of key members on the network’s architecture. The findings reveal that eliminating just the top 28% of key members causes a near-total collapse of the network, reducing the maximum connected subgraph size to almost zero. These results suggest a three-phase impact of key members on the overall network resilience. From Figures 1b-c, it becomes evident that the "key members" recognized by the deep reinforcement learning algorithm play a significantly more pivotal role in maintaining the network structure compared to randomly chosen nodes.
To assess the overlap between the "key members" and the
"pivotal players" in the co-authorship network and verify
if they support one another, the study conducts statistical
analyses. Given that real-world networks tend to display
hierarchical modularity [
Moreover, the multi-scale hierarchical modular structure observed in the co-authorship network reflects the inherent hierarchical structure of domain knowledge. Research directions, topics, subfields, and disciplines compose the knowledge hierarchy in a discipline, and researchers adaptively form co-authorships that embed research problems within diferent knowledge system scales.
Figure 1d presents the variation of club coeficients within the sub-communities of the multi-scale physical domain as a function of the proportion of deleted nodes (f). It demonstrates that each sub-community contains both global connector hubs and local provincial hubs, with global connector hubs exhibiting a stronger cohesive core structure relative to provincial hubs from the complex network system view.
Figures 1e-f summarize the density and number distribution of "pivotal role" members in the "key member" sequence groups. Key observations include: 1) A significant majority of globally and locally pivotal members are concentrated in the initial sequence subgroups of "key members." This indicates that the higher the criticality rank, the greater the proportion of "pivotal role" members. 2) There is a descending order correlation between the criticality of "pivotal role" member classification. 3) Nodes with high degree are more critical and occur in larger numbers across both the global collaborative communities and the sub-communities, demonstrating a consistent pattern in terms of importance and centrality within the network structure.
Scientific collaborative behavior is a cornerstone of largescale knowledge exploration among researchers and significantly influences their academic productivity and impact. Co-authorship networks serve as a primary analytical tool for deciphering collaboration patterns among researchers within a knowledge landscape. As network science theories and methodologies have evolved, so too has the examination of co-authorship networks’ macroscopic and mesoscopic attributes, including scale-free, small-world, modularity, and club structures. While the modularity-based and collective collaboration aspects of these networks have received substantial attention, the in-depth analysis of core structures within co-authorship networks from the modularization and collaboration perspective remains an open issue.
Recent research has demonstrated that mesoscopic core
structures have indeed been detected and studied in various
domains like biology, transportation, and power systems
[
By harnessing the interpretability of complex topology theory and the representational power of deep learning techniques, this study introduces an interpretable framework to identify and analyze the key cohesive structures in co-authorship networks. The study reveals the coexistence of two distinct core structures: local provincial hubs that primarily consolidate community members with sparse interconnections among themselves, and global connector hubs that act as bridges between researchers across diferent research areas within the collaborative community, maintaining tight interconnections.
These two types of hubs exhibit minimal overlap and possess unique network structural characteristics, exerting varying degrees of influence on other network members. The provincial hubs demonstrate a star-shaped, centralized structure, whereas the connector hubs showcase a flatter and less centralized pattern of close collaborations.
The coexistence of local centrality and global decentralization in co-authorship networks reflects a delicate balance between cost-efectiveness, stability, and flexibility within the large-scale researcher-driven knowledge exploration process. Future research aims to delve into the potential universal patterns of scientific meso-core structures across various disciplines and career stages, drawing upon comprehensive academic datasets covering multiple fields and historical periods.
This work is supported by the National Natural Science Foundation of China (Grant No.71871042 and 72371052).