This paper introduces a computational approach to characterise healthy controls and insomniacs based on graph spectral theory. Based upon expert-generated hypnograms of sleep onset periods, a network of sleep stages transitions is derived to compute four similarity distances amongst subjects' sleeping patterns. A subsequent statistical analysis is performed to differentiate the 16-subject healthy group from a 16-patient disordered cohort. Our findings demonstrated that the similarity distances based on eigenvalues determination, i.e. d1 and d4 were the most reliable and robust measures to characterise insomniacs, discriminating 93% and 87% of the affected population, respectively.