Disorders of consciousness (DOC) is a consequence of severe brain injuries. DOC diagnosis is quite challenging because it may require patient collaboration. Investigations of brain activity in resting conditions propose that healthy brain is organized into large-scale resting state networks (RSNs) of sensory/cognitive relevance. The complete set of RSN together with their corresponding interaction induce a functional network of brain connectivity (FNC). Recently, the connectivity pattern between pairs of RSNs have been explored as biomarker of loss of consciousness. The role of this FNC in the DOC conditions remains poorly understood. In this work, we propose to use a network analysis method to explore complex properties of the functional brain network induced by the connectivity among RSNs. In particular, we aim to characterize the communication quality among network nodes, which have been suggested to be linked to altered states of consciousness. The proposed approach was evaluated on a population of 27 healthy controls and 49 subjects with DOC conditions. fMRI data was obtained and processed for each subject to built a FNC at individual level. The communication quality among network nodes was quantified by using global efficiency, average characteristic path, diameter, radius, average strength and average clustering coefficient. Our results suggests that the information efficiency transfer at the global level decrease with the level the severity of the loss of consciousness condition. These results highlight the importance of graph based features to characterize brain complexity, and in particular, complex phenomena as consciousness emergence. In addition, our results can be potentially used in the development of novel methods to support diagnosis of patients with DOC conditions.