## 2 Materials and Methods
### Network Analysis  
To investigate the task-independent network properties and deepen our perception in regards of the workload-related reorganization of the underlying brain structures, we used graph theoretical analysis to detect task-independent workload-related common topological patterns. Small-world properties were originally proposed by [PERSON] and [PERSON] as the concept of connected adjacent subsets of vertices contained within the network, indicated by higher local clustering coefficient and equivalent characteristic path length compared with random networks [34]. Hence, small-world parameters--including clustering coefficient, characteristic path length, and small-worldness--were estimated in this work. The estimation of these graph theoretical metrics was performed using the Brain Connectivity Toolbox [35]. The grand network average of all trials was calculated for each subject, estimating a mean network for each task, workload level, and condition. A common sparsity was applied to all networks (i.e., keeping a specific percentage of the connections with highest weights) before computing the network metrics to ensure the equivalent wiring cost. Here, we used a wide range of sparsity (15-30% with 1% step) in order to reduce the dependency of any significant differences in network topology on the arbitrary choice of a single threshold. Then, we calculated the integral of the network metrics with respect to sparsity--i.e., the area under curve (AUC)--for the following statistical analysis [36].  
Let \(G\) be a weighted directed network with \(N\) nodes (\(N=62\) in this work), \(w_{ij}\) the weight of the edge from node \(i\) to \(j\) as calculated by PLI functional connectivity and \(H\) the adjacency matrix (\(H_{ij}=1\) if \(w_{ij}\
eq 0\)).  
Clustering coefficient quantifies the degree of local neighborhoods to form a complete network. Clustering coefficient C\({}_{i}\) of a node \(i\) is defined as [37]:  
\[C_{i}=\frac{\sum_{j\
eq i,k\
eq j}\Bigl{(}w_{ij}^{1/3}+w_{ji}^{1/3} \Bigr{)}\Bigl{(}w_{jk}^{1/3}+w_{kj}^{1/3}\Bigr{)}\Bigl{(}w_{ik}^{1/3}+w_{ki}^{ 1/3}\Bigr{)}}{2\bigl{[}(H+H^{T})_{i}((H+H^{T})_{i}-1)-2H_{ij}^{2}\Bigr{]}} \tag{2}\]The clustering coefficient C of the network is the average of the clustering coefficient across all nodes:  
\[C=\frac{1}{N}\sum_{i=1}^{N}C_{i} \tag{3}\]  
Characteristic path length quantifies how efficiently information is transferred in a network [35]. The shortest path length \(L_{ij}\) from node \(i\) to node \(j\) is defined as the minimum number of directed edges connecting the two nodes. The characteristic path length \(L\) of a network is defined as the average of the shortest path length between all node pairs:  
\[L=\frac{1}{N(N-1)}\sum_{i\
eq j}L_{ij} \tag{4}\]  
Small-worldness is a measurement to evaluate the small-world properties and is defined as the ratio of the normalized clustering coefficient to the normalized characteristic path length. The normalization is performed based on matched random networks [38]:  
\[\sigma=\frac{C}{C_{rand}}/\frac{L}{L_{rand}} \tag{5}\]  
where \(C_{rand}\) and \(L_{rand}\) represent the mean clustering coefficient and the mean characteristic path length of the random networks. Here, 100 random networks were created, which were derived from the original brain network by randomly shuffling the edges while preserving the number of nodes and edges, degree distribution, and connectedness.