Disorder of consciousness (DOC) is a consequence of severe brain injuries. Diagnosis of DOC is very challenging because it requires the patient collaboration. Research in hemodynamic brain activity in resting state conditions suggests that healthy brain is organized into large-scale resting state networks (RSNs) of sensory/cognitive relevance. Recently, relationships among these RSNs have been explored as a possible biomarker of loss of consciousness. The RSN functional connectivity is computed as the temporal relationship between pairs of RSNs time-courses. It results in the so called functional network of brain connectivity (FNC). The properties of this network in the DOC conditions remains poorly understood. In this work, we investigated some local complex network properties of the brain FNC, during altered states of consciousness. For this, we characterized a population of 49 DOC patients and 27 healthy controls. fMRI data was acquired and processed for each subject to built a FNC for each one. Network characterization was performed by computing the strength and the clustering coefficient measurements at individual level on the corresponding FNC. These nodal measurements allows to understand brain alterations of single RSN in the FNC. Our results show that strength and clustering variations may reflect brain network reconfiguration, and they may be associated to loss of consciousness states in patients with DOCs.