Limited penetrable visibility graph for establishing complex network from time series

We propose an improved visibility graph method, i.e., limited penetrable visibility graph, for establishing complex network from time series. Through evaluating the degree distributions of three visibility algorithms(visibility graph, horizontal visibility graph, limited penetrable visibility graph), we find that the horizontal visibility graph cannot distinguish signals from periodic, fractal, and chaotic systems; for fractal signal, the degree distributions obtained from visibility graph and limited penetrable visibility both can be well fitted to a power-law(scale-free distribution), but the anti-noise ability is not good; for periodic and chaotic signals, the limited penetrable visibility graph shows better anti-noise ability than visibility graph. In this regard, we use the limited penetrable visibility graph to extract the network degree distribution parameters from conductance fluctuating signals measured from oil-gas-water three-phase flow test. The results indicate that combination parameters of network degree distribution can be used to classify typical three phase flow patterns, e.g., oil-in-water bubble flow, bubble-slug transitional flow and slug flow.