We optimize and design a new half-ring conductance sensor for measuring two-phase flow in a small diameter pipe. Based on the experimental signals measured from the designed sensor, we using the limited penetrable visibility graph we proposed construct complex networks for different flow patterns. Through analyzing the constructed networks, we find that the joint distribution of the allometric scaling exponent and the average degree of the network allows distinguishing different gas-liquid flow patterns in a small diameter pipe. The curve peak of the degree distribution allows uncovering the detailed features of the flow structure associated with the size of gas bubbles, the average degree of the network can reflect the macroscopic property of the flow behavior, The allometric scaling exponent is very sensitive to the complexity of fluid dynamics and allows characterizing the dynamic behaviors in the evolution of different flow patterns. In this regard, limited penetrable visibility graph analysis of fluid signals can provide a new perspective and a novel tool for uncovering the dynamical mechanisms governing the formation and evolution of different flow patterns.