Early psychiatry investigated dreams to understand psychopathologies. Contemporary psychiatry, which neglects dreams, has been criticized for lack of objectivity. In search of quantitative insight into the structure of psychotic speech, we investigated speech graph attributes (SGA) in patients with schizophrenia, bipolar disorder type I, and non-psychotic controls as they reported waking and dream contents. Schizophrenic subjects spoke with reduced connectivity, in tight correlation with negative and cognitive symptoms measured by standard psychometric scales. Bipolar and control subjects were undistinguishable by waking reports, but in dream reports bipolar subjects showed significantly less connectivity. Dream-related SGA outperformed psychometric scores or waking-related data for group sorting. The results demonstrate the feasibility of the differential diagnosis of psychosis based on the analysis of dream graphs, pointing to a fast, low-cost and language-invariant tool for psychiatric diagnosis and the objective search for biomarkers. I will also briefly discuss the extension of these graph-theoretical ideas to the traditional fluency test in the diagnostic of Alzheimer’s disease, as well as their correlation with measures of cognitive and academic performance of children ages 6-8.