*Article* **Building Networks with a New Cross-Bubble Transition Entropy for Quantitative Assessment of Mental Arithmetic Electroencephalogram**

**Xiaobi Chen 1, Guanghua Xu 1,2,\*, Sicong Zhang 1, Xun Zhang <sup>1</sup> and Zhicheng Teng <sup>1</sup>**

	- **\*** Correspondence: ghxu@xjtu.edu.cn

**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.

**Keywords:** cognitive load; coupling; bubble entropy; transition network
