Table 3.

Summary of the network metrics for cognitive control properties across states

Metric name	Formula	Measures; property	Parameter-space?	Relies on predefinedpartition?
GVC	${GVC}_n=\frac{1}{N}\sum _{i=1}^n\sqrt{\frac{\sum _{l=1}^T{({FC}_{il}-{\overline{x}}_{FCl})}^2}{T-1}}$	Variable FC across tasks; flexible hubs	No	No
BVC	${BVC}_n=\frac{1}{N\prime }\sum _{i^{\prime }=1}^{n\prime }\sqrt{\frac{\sum _{l=1}^T{({FC}_{i^{\prime }l}-{\overline{x}}_{FCl\prime })}^2}{T-1}}$	Variable FC across tasks, between-network;flexible hubs	No	Yes
Network partition deviation(deviation)	${deviation}_n=1-\left[\frac{\sum _{l=1}^T\left[\left(max\left(\frac{{\sum }_{rS=1}^c{FC}_{cl}}{C}\right)\right)\in rS\right]}{T}\right]$	Network preference changes vs intrinsic (rest);reassignment profile	Minimal	Yes

GVC (Cole et al., 2013b), BVC, and network partition deviation (novel; named in column 1) are described in terms of the following. Column 2, Their mathematical or algorithmic formulae. All equation symbols are expressed consistently. Formula terms: n = brain regions; N = number of regions; i = region 1; l = task 1; T = tasks; FC = weighted adjacency matrix; x-barr = mean; FC_il = edge weight, per region, per task; FCl = FC matrix, per task; n' = out-of-network regions; N' = number of out-of-network regions; i' = region 1, out-of-network; l' = task 1, out-of-network regions only; FC_i'l = edge weight, per out-of-network region, per task; FCl' = FC matrix, out-of-network regions only, per task; c = network regions; C = number of network regions; rS = predefined partition; FC_cl = edge weights per network-region, per task. Column 3, What each metric measured. This was how results were interpreted, and mechanisms or properties were framed. Column 4, If each metric relied on user-chosen parameters (e.g., had a parameter-space). Column 5, If each metric relied on a predefined network partition (also see Materials and Methods).