###### Abstract
There is a growing interest in the cognitive load assessment through the construction of complex networks, and various methods have been proposed to convert time series into networks [27; 28; 29; 30]. Complex networks constructed using different network construction algorithms may have distinct, significantly different properties [31]. A variety of methods have been proposed so far to define the concept of connectivity between nonlinearly coupling components and investigate the characteristics of the topological properties of networks. Among different methods, for example, the mutual information (MI) (including its time-delayed version) [32; 33], transfer entropy (TE) [34], inner composition alignment (IOTA) [35] and cross-sample entropy (CSE) [36], the TE is widely used in particular as a nonparametric measure that does not rely on any assumption of some model and can capture the directional and dynamic interaction between the different components of a time series [37; 38]. However, in practice, an unavoidable pitfall of TE is that robust estimation of the interactions requires long-term data recordings. In order to meet the need for interaction estimation using finite data samples, [PERSON] et al. proposed the CPE by fusing inner composition alignment (IOTA) and permutation entropy, and validated it in financial time series analysis [39], noting that CPE was simple, stable, and efficient. In the original CPE method, only the probability distribution of the symbols after coarse graining of the affected time series is considered during the calculation of entropy, ignoring the transition relationship between the symbols in the temporal domain. For example, given the symbolized set A = [2 2 4 3 5 1 2] and B = [1 2 2 5 3 2 4 ], the probability distributions of the elements in set A and set B are the same and, therefore, the original CPE method would obtain the same entropy value. In addition, like other nonlinear measures, the CPE method involves the manual selection of parameters to ensure the effectiveness of the results. In order to address these issues, a new method to construct the complex network based on the cross-transition network was proposed in this study to assess cognitive load. The novelty of the method lies in incorporating the advantages of transition network and bubble entropy [40] into the CPE to estimate the coupling strength of two time series from a cross-network perspective. The node-wise out-link transition entropy of two time series cross-transition networks was proposed as the edge weights between two time series to construct the complex network, and the network parameters were extracted as a quantitative measurement of the cognitive load. Referring to the symbolization process of the bubble entropy, the number of swaps required to sort the phase space reconstruction vectors of the affected time series in the ascending order was used instead of the number of intersections calculated by the OITA method in the original CPE. In order to verify the effectiveness of the proposed method, the unidirectional coupled Honen model with different coupling strengths was used, and the results were compared with those obtained using the original CPE. The proposed method and the original CPE method were further compared by constructing the complex network on the realistic EEG recordings from the mental arithmetic task. The significance of the selected network indicator and the capability of the proposed method to differentiate different levels of brain cognitive load were verified using the nonparametric permutation test. The contributions of this paper are as follows. 1. Based on the cross-transition network, a novel method is proposed that reflects the information interaction between two time series in more detail. 2. The symbolization process with reference to the bubble entropy minimizes the effect of parameter setting on the analysis results. 3.