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

It is possible to investigate emergence in many real systems using time-ordered data. However, classical time series analysis is usually conditioned by data accuracy and quantity. A modern method is to map time series onto graphs and study these structures using the toolbox available in complex network analysis. An important practical problem to investigate the criticality in experimental systems is to determine whether an observed time series is associated with a critical regime or not. We contribute to this problem by investigating the mapping called visibility graph (VG) of a time series generated in dynamical processes with absorbing-state phase transitions. Analyzing degree correlation patterns of the VGs, we are able to distinguish between critical and off-critical regimes. One central hallmark is an asymptotic disassortative correlation on the degree for series near the critical regime in contrast with a pure assortative correlation observed for noncritical 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. The determination of critical behavior converges very quickly in higher dimensions, where many complex system dynamics are relevant.