32While long-range cortico-cortical functional connectivity has been reported by several studies 33 as a necessary condition of conscious state, precise empirical evidence is still scarce. In the 34 present work we provide such a direct and conclusive evidence in a set of three experiments. 35 In the two first experiments intracranial-EEG was recorded during four distinct states in the 36 same individuals: conscious wakefulness (CW), rapid-eye-movement sleep (REM), stable 37 periods of slow-wave sleep (SWS) and deep propofol anaesthesia (PA). We discovered that 38 long-range FC, computed by the weighted Symbolic-Mutual-Information (wSMI) in the 2-39 5Hz frequency band was a specific marker of conscious states that could discriminate CW and 40 REM from SWS and PA. In the third experiment, we generalized this original finding on a 41 large cohort of brain-injured patients by revealing that wSMI in the 2-5 Hz range was also 42 able to accurately discriminate patients in the vegetative state (or unresponsive wakefulness 43 syndrome) from patients in the minimally conscious state. Taken together the present results 44 suggest that 2-5Hz FC is a new and robust signature of conscious states. 45 46 50 Crone et al., 2014; Dehaene and Changeux, 2011; Dehaene and Naccache, 2001), this 51 property remains highly debated regarding : (i) the long-range (Laureys and Schiff, 2012) 52 versus short-range type of functional connectivity (Lamme, 2006) (ii) the relevant frequencies 53 involved in this cortico-cortical connectivity, with contradicting proposals ranging from ultra-54 slow (<0.01Hz) (Barttfeld et al., 2015), to slow (0.5-4Hz) (He et al., 2008; He and Raichle, 55 2009), or even faster theta, alpha and gamma-band rhythms (Schiff et al., 2014), and (iii) the 56 general value of this property when comparing various conscious and unconscious states.57In order to address these important and unsolved questions, we explored cortico-cortical 58 connectivity on direct intracranial EEG (iEEG) recordings performed in the same subjects 59 across various conscious and unconscious states. More precisely, we recorded iEEG in 12 60 drug-resistant epileptic patients undergoing a stereoelectroencephalography (SEEG) for pre-61 surgical evaluation with large and brain-scale implantations. Each patient was recorded in two 62 3 states that are associated with conscious experience (conscious wakefulness (CW) and rapid-63 eye movement sleep (REM) that is typically associated with conscious dreaming), as well as 64 in two unconscious states: very stable periods of slow-wave sleep (SWS) that are usually free 65 of conscious dreaming (Siclari et al., 2017), and deep propofol anaesthesia (PA). 66 We estimated cortico-cortical connectivity by computing the weighted symbolic mutual 67 information (wSMI) in various frequency bands. We previously conceived wSMI and used 68 this measure to distinguish conscious and minimally conscious (MCS) patients from 69 vegetative state/unresponsive wakefulness syndrome (VS/UWS) patients (King et al., 2013). 7...