Coordinated patterns of cortical morphology have been described as structural graphs and previous research has demonstrated that properties of such graphs are altered in Alzheimer's disease (AD). However, it remains unknown how these alterations are related to cognitive deficits in individuals, as such graphs are restricted to group-level analysis. In the present study we investigated this question in single-subject grey matter networks. This new method extracts large-scale structural graphs where nodes represent small cortical regions that are connected by edges when they show statistical similarity. Using this method, unweighted and undirected networks were extracted from T1 weighted structural magnetic resonance imaging scans of 38 AD patients (19 female, average age 72±4 years) and 38 controls (19 females, average age 72±4 years). Group comparisons of standard graph properties were performed after correcting for grey matter volumetric measurements and were correlated to scores of general cognitive functioning. AD networks were characterised by a more random topology as indicated by a decreased small world coefficient (p = 3.53×10(-5)), decreased normalized clustering coefficient (p = 7.25×10(-6)) and decreased normalized path length (p = 1.91×10(-7)). Reduced normalized path length explained significantly (p = 0.004) more variance in measurements of general cognitive decline (32%) in comparison to volumetric measurements (9%). Altered path length of the parahippocampal gyrus, hippocampus, fusiform gyrus and precuneus showed the strongest relationship with cognitive decline. The present results suggest that single-subject grey matter graphs provide a concise quantification of cortical structure that has clinical value, which might be of particular importance for disease prognosis. These findings contribute to a better understanding of structural alterations and cognitive dysfunction in AD.