Attention-deficit /hyperactivity disorder (ADHD) is a common neurodevelopmental syndrome characterized by age-inappropriate levels of motor activity, impulsivity and attention. The aim of the present study was to study diurnal variation of motor activity in adult ADHD patients, compared to healthy controls and clinical controls with mood and anxiety disorders. Wrist-worn actigraphs were used to record motor activity in a sample of 81 patients and 30 healthy controls. Time series from registrations in the morning and evening were analyzed using measures of variability, complexity and a newly developed method, the similarity algorithm, based on transforming time series into graphs. In healthy controls the evening registrations showed higher variability and lower complexity compared to morning registrations, however this was evident only in the female controls. In the two patient groups the same measures were not significantly different, with one exception, the graph measure bridges. This was the measure that most clearly separated morning and evening registrations and was significantly different both in healthy controls and in patients with a diagnosis of ADHD. These findings suggest that actigraph registrations, combined with mathematical methods based on graph theory, may be used to elucidate the mechanisms responsible for the diurnal regulation of motor activity.

Depression and schizophrenia are defined only by their clinical features, and diagnostic separation between them can be difficult. Disturbances in motor activity pattern are central features of both types of disorders. We introduce a new method to analyze time series, called the similarity graph algorithm. Time series of motor activity, obtained from actigraph registrations over 12 days in depressed and schizophrenic patients, were mapped into a graph and we then applied techniques from graph theory to characterize these time series, primarily looking for changes in complexity. The most marked finding was that depressed patients were found to be significantly different from both controls and schizophrenic patients, with evidence of less regularity of the time series, when analyzing the recordings with one hour intervals. These findings support the contention that there are important differences in control systems regulating motor behavior in patients with depression and schizophrenia. The similarity graph algorithm we have described can easily be applied to the study of other types of time series.

Cardiac inter‐beat intervals (IBIs) are considered to reflect autonomic functioning and self‐regulatory abilities and are often investigated by traditional time‐ and frequency domain analyses. These analyses investigate IBI fluctuations across relatively long time series. The similarity graph algorithm is a nonlinear method that analyzes segments of IBI time series (i.e., time windows)—possibly being more sensitive to transient and spontaneous IBI fluctuations. We hypothesized that the similarity graph algorithm would detect differences between Attention‐Deficit/Hyperactivity Disorder (ADHD) and control groups. Resting electrocardiogram (ECG) recordings were collected in 10–18‐year‐olds with ADHD (n = 37) and controls (n = 36). IBIs were converted to graphs that were subsequently investigated for similarity. We varied the criterion for defining IBIs as similar, assessing which setting best distinguished ADHD and control groups. Using this setting, we applied the similarity graph algorithm to time windows of 2–5, 6–13 and 12–25 s, respectively. We also performed traditional IBI analyses. Independent samples t tests assessed group differences. Results showed that a 1.5% criterion of similarity and a time window of 2–5 s best distinguished adolescents with ADHD and controls. The similarity graph algorithm showed a higher number of edges, maximum edges and cliques, and lower edges10+10/edges2+2 in the ADHD group compared to controls. The results suggested more similar IBIs in the ADHD group compared to the controls, possibly due to altered vagal activity and less effective regulation of heart rate. Traditional analyses did not detect any group differences. Consequently, the similarity graph algorithm might complement traditional IBI analyses as a marker of psychopathology.