We investigated the relationships between grey matter graph properties and cognitive impairment in a sample of 215 patients with Alzheimer's disease (AD) and whether age of disease onset modifies such relationships. We expected that more severe cognitive impairment in AD would be related to more random graph topologies. Single-subject grey matter graphs were constructed from T1-weighted magnetic resonance imaging scans. The following global and local graph properties were calculated: betweenness centrality, normalised clustering coefficient γ and normalised path length λ. Local clustering, path length and betweenness centrality measures were determined for 90 anatomically defined areas. Regression models with as interaction term age of onset (i.e., early onset when patients were =< 65 and late onset when they were > 65 years old at time of diagnosis) * graph property were used to assess the relationships between cognitive functioning in five domains (memory, language, visuospatial, attention and executive). Worse cognitive impairment was associated with more random graphs, as indicated by low γ, λ and betweenness centrality values. Three interaction effects for age of onset * global graph property were found: Low γ and λ values more strongly related to memory impairment in early onset patients; low beta values were significantly related to impaired visuospatial functioning in late onset patients. For the local graph properties, language impairment showed the strongest relationship with decreased clustering coefficient in the left superior temporal gyrus across the entire sample. Our study shows that single-subject grey matter graph properties are associated with individual differences in cognitive impairment.