## 4 Quantitative Analysis  
Summarizing the publication trends in the field of digital twin software solutions with industrial robot applications can provide valuable insights into the technological advancements documented in the literature. Figure 3 illustrates the patterns observed in the cited sources, highlighting the progression of research in this area. From the comprehensive literature search conducted, a total of 159 articles were selected for quantitative evaluation. It is clear from the figure that digital twin research has gained popularity as a tool for tracking conditions, notifying asset managers of necessary repairs, and facilitating real-time data transfer to virtual models since 2018.  
_Density Visualization of Keyword Co-Occurrence Analysis_  
Co-occurrence analysis of keywords was employed to examine the relationships and patterns within the collected data from the literature review [67], providing insights into  
Figure 3: Number of digital twin-related publications per year based on keyword co-occurrence: ‘digital twin’, ‘collaborative robotics’, and ‘operational efficiency’.  
the concepts and structure conveyed by these keywords. The analysis involves representing keywords as nodes and visualizing their co-occurrence, highlighting the density and frequency of specific keyword combinations. This approach enhances our understanding of the interconnections and prevalence of certain concepts, enabling a comprehensive exploration of the literature and identifying key themes and relationships within the research field. Figure 4 illustrates a density visualization technique employed to gain a holistic view of the knowledge structure based on keyword co-occurrence analysis. This approach utilizes variables such as node-to-node distance and weight (representing the number of co-occurrences) to determine the density of each node, providing a snapshot of the entire structure and highlighting significant points within the scholarly work [65]. The intensity of the colors in the visualization is based on factors such as the proximity of research works, the distance between nodes, and their level of interconnectedness. The study's findings reveal that concepts like the Internet of Things, machine learning, and industry 4.0 exhibit substantial correlation and significance, as indicated by their positioning in the middle of the map, consistent with the literature review. However, automation, information management, deep learning, and security have received comparatively less attention and development.  
Table 2 shows the highest cited research publications in the Industrial Digital Twin space At the time of this publication (excluding reviews and survey-based publications). This search was conducted in Scopus using \"Industrial Digital Twins\" as the search keywords. These papers share similar foundations, such as the complete definitions of a DT, the development of a framework for creating and using a DT, and a case study which reflects the exploration of the framework and approach that was expressed. Moreover, each of these publications highlight the need for more detailed and scrutinized experimentation in the DT domain, evaluating more use cases through experimentation.  
Figure 4: Cloud density visualization of the co-occurrence of keywords used in the literature search.