Functional Near InfraRed Spectroscopy (fNIRS) connectivity analysis is often performed using the measured oxy-haemoglobin (HbO2) signal, while the deoxy-haemoglobin (HHb) is largely ignored. The in-common information of the connectivity networks of both HbO2 and HHb is not regularly reported, or worse, assumed to be similar. Here we describe a methodology that allows the estimation of the symmetry between the functional connectivity (FC) networks of HbO2 and HHb and propose a differential symmetry index (DSI) indicative of the in-common physiological information. Our hypothesis is that the symmetry between FC networks associated with HbO2 and HHb is above what should be expected from random networks. FC analysis was done in fNIRS data collected from six freely-moving healthy volunteers over 16 locations on the prefrontal cortex during a real-world task in an out-of-the-lab environment. In addition, systemic data including breathing rate (BR) and heart rate (HR) were also synchronously collected and used within the FC analysis. FC networks for HbO2 and HHb were established independently using a Bayesian networks analysis. The DSI between both haemoglobin (Hb) networks with and without systemic influence was calculated. The relationship between the symmetry of HbO2 and HHb networks, including the segregational and integrational characteristics of the networks (modularity and global efficiency respectively) were further described. Consideration of systemic information increases the path lengths of the connectivity networks by 3%. Sparse networks exhibited higher asymmetry than dense networks. Importantly, our experimental connectivity networks symmetry between HbO2 and HHb departs from random (t-test: t(509) = 26.39, p < 0.0001). The DSI distribution suggests a threshold of 0.2 to decide whether both HbO2 and HHb FC networks ought to be studied. For sparse FC networks, analysis of both haemoglobin species is strongly recommended. Our DSI can provide a quantifiable guideline for deciding whether to proceed with single or both Hb networks in FC analysis.