  This paper addresses the question of the brain's critical dynamics after an
injury such as a stroke. It is hypothesized that the healthy brain operates
near a phase transition (critical point), which provides optimal conditions for
information transmission and responses to inputs. If structural damage could
cause the critical point to disappear and thus make self-organized criticality
unachievable, it would offer the theoretical explanation for the post-stroke
impairment of brain function. In our contribution, however, we demonstrate
using network models of the brain, that the dynamics remain critical even after
a stroke. In cases where the average size of the second-largest cluster of
active nodes, which is one of the commonly used indicators of criticality,
shows an anomalous behavior, it results from the loss of integrity of the
network, quantifiable within graph theory, and not from genuine non-critical
dynamics. We propose a new simple model of an artificial stroke that explains
this anomaly. The proposed interpretation of the results is confirmed by an
analysis of real connectomes acquired from post-stroke patients and a control
group. The results presented refer to neurobiological data; however, the
conclusions reached apply to a broad class of complex systems that admit a
critical state.
