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We propose a reliable method for constructing complex network from a time series based on phase space reconstruction and construct complex flow networks using the conductance fluctuating signals measured from gas-liquid two-phase flow experiment. After detecting the node strength distribution of the networks, we show that the strength distribution of the resulting networks can be well fitted with a power law. Furthermore, we using the method of chaotic recurrence plot explore the physical implications of network strength distribution. To investigate the dynamic characteristics of gas-liquid flow, we construct 50 complex flow networks under different flow conditions, and find that the power-law exponent, which is sensitive to the flow pattern transition, can really characterize the nonlinear dynamics of gas-liquid two-phase flow. In this paper, from a new perspective, we not only propose a novel method to study nonlinear time series signals in practice, but also indicate that complex network may be a powerful tool for exploring complex nonlinear dynamic systems.