## 4 Case Study
### Case Study Findings  
This section reports the main findings we obtained in the case study following the procedures described in Appendix A. Thus, for more details on the methodology and measurements exploited, please refer to such section.  
Figure 1 displays the plot of the surgery network (left panel) and the correlations between glitches and centrality measures (right panel). Such values were computed by means of the classical Pearson correlation.  
Figure 1: The network projection of the surgery rooms interactions (left panel) and correlations between glitches and centrality measures. In the left panel, red nodes indicate the occurrence of a glitch; in the right panel, for the \(p\)-values, we obtained 0.00234 for glitch–transitivity, 0.00318 for glitch–betweenness, 0.00592 for glitch–closeness, 0.00926 for glitch–degree, 0.0119 for glitch–pagerank, 0.0127 for glitch–eigenvector centrality, and 0.0209 for glitch–authority, while we obtained 0.347 for glitch–Bonacich index and 0.393 for glitch–corens (note that these last two correlations are depicted with the boxplot filled in grey).  
The first main observable network characteristic is the distribution of the degree across the network. It results in a random distribution with a mean of 32.96 connections for each node. The absence of any notable degree distribution (e.g., log-normal, etc.) highlights the fact that the network lacks the emergence of hubs, i.e., a similar number of surgeons have operated and an excessive unbalanced workload does not emerge. Since this latter may be identified as a problem associated with incidents [1; 54; 55], we cannot sustain the main correlation between glitches and team fatigue.  
Another argument which brings us in the direction of the absence of preferential staff in terms of an elite subgroup of surgeons as well as in terms of team mix--seniors with other senior members instead of seniors with junior members--is a neutral value of the degree assortativity (see Appendix A for further details).  
In this case study, the randomness of the degree distribution raises some challenges for the understanding of deviations from the expected path and the unveiling of self-organised patterns, mainly caused by the difficulties in knowing which dyads dominate in the network.  
However, the centrality measures provided interesting results, emphasising a relationship between surgical team network and surgical performance, evaluated in terms of glitch occurrence. Specifically, the negative correlation of transitivity and the positive correlation of betweenness centrality (see Figure 1, right panel) with the glitches indicate that the emergence of stable groups of surgeons might not be a good strategy for improving surgical performances, at least in high routine surgery. These measures appear to reveal that a low variability in the operating team composition--i.e., a potential attractor state--establishes a path dependence that increases the probability of surgeries to experience a glitch in the future. Thus, surgeons should work with different colleagues, instead of forming sub-groups that work continuously together.  
The reasons behind such evidence may be related to two main aspects. Firstly, if the surgeons taking part in surgery have had different surgery experiences, they will be able to face a wide spectrum of potential and unplanned issues [56; 57]. In addition, by collaborating with different colleagues, surgeons can observe and learn relevant \"best practices\" to apply in the future [58; 59]. The second reason is related to the fact that the operating team very often establishes a very high \"intimacy\" so that they tend to pay less attention to the specific tasks and to be more prone to distractions, increasing the probability to face a glitch [1; 60; 61]. In these cases, the team members might introduce a novel complex cause-effect relationship that alters the dynamics and, finally, the team performance. This aspect seems to assume a particularly significant role in routine surgeries, as breast surgery [4; 62; 63; 64; 65].