###### Abstract  
The complex network nature of human brains has led an increasing number of researchers to adopt a complex network to assess the cognitive load. The method of constructing complex networks has a direct impact on assessment results. During the process of using the cross-permutation entropy (CPE) method to construct complex networks for cognitive load assessment, it is found that the CPE method has the shortcomings of ignoring the transition relationship between symbols and the analysis results are vulnerable to parameter settings. In order to address this issue, a new method based on the CPE principle is proposed by combining the advantages of the transition networks and the bubble entropy. From an interaction perspective, this method suggested that the node-wise out-link transition entropy of the cross-transition network between two time series is used as the edge weight to build a complex network. The proposed method was tested on the unidirectional coupled Henon model and the results demonstrated its suitability for the analysis of short time series by decreasing the influence of the embedding dimension and improving the reliability under the weak coupling conditions. The proposed method was further tested on the publicly available EEG dataset and showed significant superiority compared with the conventional CPE method. c 2022 2  
resonance imaging (fMRI), electrocorticography (ECoG), or electroencephalography (EEG) are closely correlated with brain status and can provide a useful way to assess cognitive load [14; 15; 16; 17; 18]. Among these physiological signals, EEG has been widely concerned by researchers because of its high time resolution, noninvasiveness, convenience, security, cheapness, and portability [19; 20]. In general, the EEG signal is nonstationary and nonlinear. Linear analysis techniques in the time-frequency domain can be used to detect rhythmic oscillations, but the contained nonlinear information cannot be effectively extracted [21]. Therefore, many scholars have attempted to extract various nonlinear parameters from EEG signals and combine them with the machine learning technique in order to effectively capture the subtle information related to the physiological states. [PERSON] et al. used the empirical mode decomposition (EMD) and the variational mode decomposition (VMD) to decompose the EEG signals, respectively, and then used the second-order difference plots for feature mining of the decomposed intrinsic modes. The results showed that alcoholic (A) and nonalcoholic (NA) subjects could be accurately classified when using short-duration EEG recordings [22]. [PERSON] et al. proposed extracting [PERSON] and Higuchi's fractal dimensions, dispersion entropy, and bubble entropy from the sub-band of a single-channel frontal EEG recording to construct the nonlinear feature set and then differentiate between the arousal and the sleep stage I [23]. [PERSON] et al. used seven nonlinear parameters, including the sample entropy (SampEn), fractal dimension (FD), higher-order spectrum (HOS), maximum Lyapunov index (LLE), Kolmogorov complexity (KC), Hurst index (HE), and the band power of the EEG signal in sleep stage 2 and 3 as the features to classify between patients with fibromyalgia and healthy controls. The accuracy, sensitivity, and specificity of the classification results were 96.15%, 96.88%, and 95.65%, respectively [24]. The nonlinear parameters in the above-mentioned methods were taken from individual EEG channels and involve no information on the interaction between different channels. However, previous research has shown that the brain should be treated as a complex network system based on the many features it shares with networks of other biological and physical systems [25]. Complex network analysis is a powerful technique based on the graph theory that typically uses a small number of valid and reliable measures to capture the features of the brain network [26].