Sequential limited penetrable visibility-graph motifs

Network motif provides a powerful tool to characterize the recurrent and statistically significant microstructure of networks. We in this paper develop the sequential motifs in limited penetrable visibility graph and introduce the motif entropy as the quantitative index to estimate the complexity of network structure. The visibility-graph motif entropy and limited penetrable visibility-graph motif entropy of graphs associated with chaotic time series and fractional Brownian motion are studied. The results suggest that limited penetrable visibility-graph motif entropy presents the better robustness than visibility-graph motif entropy and potential ability in distinguishing different time series. In the end, the limited penetrable visibility-graph motif entropy and visibility-graph motif entropy are applied to mine the information about different flow patterns contained in the ultrasonic sensor signals of oil-in-water two-phase flow.