Graph theory has been playing an increasingly important role in understanding the organizational properties of brain networks, subsequently providing new tools for the search of neural correlates of consciousness, particularly in the context of patients recovering from severe brain injury. However, this approach is not without challenges, as it usually relies on arbitrarily fixing a threshold in order to retain the strongest connections proportionally equal across subjects. This method increases the comparability between individuals or groups but it risks the inclusion of false positive and therefore spurious connections, especially in the context of brain disorders. Resting state data acquired in 25 coma patients and 22 healthy subjects was compared. We obtained a representative fixed density of significant connections by first applying a p-value-based threshold on healthy subjects' networks and then choosing a threshold at which all individuals exhibited meaningful connections. The obtained threshold (i.e. 10%) was used to construct graphs in the patient group. The findings showed that coma patients have lower number of significant connections with approximately 50% of them not fulfilling the criteria of the fixed density threshold. The remaining patients with relatively preserved global functional connectivity had sufficient significant connections between regions, but showed signs of major whole-brain network reorganization. These results warrant careful consideration in the construction of functional connectomes in patients with disorders of consciousness and set the scene for future studies investigating potential clinical implications of such an approach.