Recently, there has been increasing interest in applying graph theory to the quantitative analysis of brain functional networks, while phase synchronization (PS) analysis has been demonstrated to be a useful method to infer functional connectivity with multichannel neural signals, e.g., electroencephalogram (EEG). In this paper, we focus on the case that the number of channels in EEG data is not adequate for the use of graph theory analysis. The degree of network-links (DNLs), an index based on the PS analysis of all the EEG wave pairs, is proposed to study the relevant and the overall characteristics of the brain. With the help of a novel division to the frequency range 0.5–30 Hz, we analyze the DNLs in different frequency bands of the EEG signals. As a comparison, a frequency band analysis of the relative power spectrum is conducted. The results demonstrate that when the cerebral infarction (CI) patients and normal control people are analyzed, there is a need for the reasonable length of EEG data to quantify the differences between different dynamical systems; under a reasonable data length, the frequency band (19–24 Hz) yields the best accuracy for diagnosing CI, which lies within the classical beta band (13–30 Hz); furthermore, only in the 19–24 Hz band, as for the values of relative power spectrum, in each EEG channel, there presents a similar relationship between the CI group and control group. The experimental results suggest that 19–24 Hz should be the optimal range for the diagnosis of CI, further the DNLs calculated within this band serve as an assist indicator in the CI diagnosis.

Based on the method of multi-scale space (Pm, Gm) and data surrogating test, time-irreversibility analysis is applied to the heart rate variabilities (HRVs) from different crowds and different states, awake and asleep respectively, of healthy youths. The results show that i) the HRVs of healthy crowed have irreversible dynamics prevailingly, while the irreversibility decreases but does not disappear with aging or heart disease appearing. For example, most (more than 75%) of the congestive heart failure (CHF) patients still have irreversible dynamics; ii) for HRVs of healthy crowd, irreversible dynamics presents the daytime/nighttime rhythms and their significant difference between in daytime and in nighttime. And a stronger irreversibility is detected in nighttime. HRV is generated by the cardiac dynamic system, in which regulations usually perform via multiple feedback loops with different delays. Therefore, in order to arrive at a reliable conclusion, multi-scale strategy and data surrogating test are suggested to serve as the two elements for the detection of time irreversibility in HRV. The proposed method combines these two elements and reaches a conclusion consistent with the conclusions in previous reports.