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Gas–liquid two-phase flow widely exits in production and transportation of petroleum industry. Characterizing gas–liquid flow and measuring flow parameters represent challenges of great importance, which contribute to the recognition of flow regime and the optimal design of industrial equipment. In this paper, we propose a novel complex network-based deep learning method for characterizing gas–liquid flow. Firstly, we map the multichannel measurements to multiple limited penetrable visibility graphs (LPVGs) and obtain their degree sequences as the graph representation. Based on the degree distribution, we analyze the complicated flow behavior under different flow structures. Then, we design a dual-input convolutional neural network to fuse the raw signals and the graph representation of LPVGs for the classification of flow structures and measurement of gas void fraction. We implement the model with two parallel branches with the same structure, each corresponding to one input. Each branch consists of a channel-projection convolutional part, a spatial–temporal convolutional part, a dense block and an attention module. The outputs of the two branches are concatenated and fed into several full connected layers for the classification and measurement. At last, our method achieves an accuracy of 95.3% for the classification of flow structures, and a mean squared error of 0.0038 and a mean absolute percent error of 6.3% for the measurement of gas void fraction. Our method provides a promising solution for characterizing gas–liquid flow and measuring flow parameters.