## 3 Results
### Integrated Analysis of Connectivity  
The networks in Figure 6 shows the links existing in the corresponding pair of HbO\({}_{2}\) and HHb networks for each condition. Also, Figure 6 depicts the FC networks obtained with and without the systemic factors (heart rate and breathing rate). Regarding in-common links, the inclusion of systemic variables increases the number of such relations during BL, OG, and NonSocPM conditions by 4, 8, and 2 increments respectively. The OGc condition remains unchanged and SocPM condition diminished in 2 links. More connections were found in the PM blocks (Figure 6c,d,h,i) in respect to the OG blocks (Figure 6b,g,e,j). These connections are more observed between the two hemispheres and, some of them, at the left and right lateral prefrontal cortex (PFC). Also, Figure 6b,g shows a set of connections between the close channels 13-14, 15-16, 2-5, 7-8, 9-12 within the same region. On the other hand, connections between corresponding channels (Ch. 2-14, 4-16, 3-10, 7-13) in the two lateral PFC were also found (Figure 6d,i). This could be caused by a higher involvement of lateral PFC, which has been observed in prospective memory tasks and a major involvement of medial PFC is related to OG activities [31]. Table 1 summarises the changes in density and symmetry values from the combined networks presented in Figure 6. The five FC networks exhibits an increase in density of 2%, 3%, 2%, 2% and 5% for BL, OG, SocPM, NonSocPM, and OGc conditions respectively. In terms of Jaccard symmetry, BL, OG, and NonSocPM conditions showed increasing values of 4%, 8%, and 1% respectively while the SocPM and OGc conditions decreased by 4% and 3% respectively. Unlike random networks, fNIRS FC networks tends to have absolute low values of symmetry. Thus, the addition of the systemic information produced small changes in both symmetry and density.  
Finally, Figure 7 presents the GE and MOD with respect to density. In general, a contrapositive behaviour for SocPM and BL networks was observed (greater values of GE and smaller values of MOD). This trend is somewhat expected; fully connected networks have maximum GE and minimal modularity, and in the opposite extreme, strictly modular networks have little efficiency. More specifically for GE, a positive trend is observed and roughly the BL-OG-OGc-NonSocPM-SocPM order can be recognised. On the other hand, for MOD results a negative trend can be seen with almost the opposite order. Also, more than the half of the HbO\({}_{2}\) networks were found to be over the mean MOD value.  
Figure 6: Combined HbO\({}_{2}\)-HHb functional connectivity networks recovered from a virtual-typical-subject. Top (**a**–**e**) and bottom (**f**–**j**) rows show the networks without and with systemic variables information respectively. From left to right, columns representing the conditions: baseline (**a**,**f**), ongoing (**b**,**g**), social prospective memory (**c**,**h**), non-social prospective memory (**d**,**i**), and ongoing contaminated (**e**,**j**). Functional links determined from HbO\({}_{2}\) and HHb are shown in solid red and dashed blue respectively and in-common links in bold magenta.