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It is possible to investigate emergence in many real systems usingtime-ordered data. However, classical time series analysis is usuallyconditioned by data accuracy and quantity. A modern method is to map timeseries onto graphs and study these structures using the toolbox available incomplex network analysis. An important practical problem to investigate thecriticality in experimental systems is to determine whether an observed timeseries is associated with a critical regime or not. We contribute to thisproblem by investigating the mapping called visibility graph (VG) of a timeseries generated in dynamical processes with absorbing-state phase transitions.Analyzing degree correlation patterns of the VGs, we are able to distinguishbetween critical and off-critical regimes. One central hallmark is anasymptotic disassortative correlation on the degree for series near thecritical regime in contrast with a pure assortative correlation observed fornoncritical dynamics. We are also able to distinguish between continuous(critical) and discontinuous (noncritical) absorbing state phase transitions,the second of which is commonly involved in catastrophic phenomena. Thedetermination of critical behavior converges very quickly in higher dimensions,where many complex system dynamics are relevant.

Visibility graphs of critical and off-critical time series for absorbing state phase transitions