  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.
