  Microscopic structural damage, such as lesions in neural systems or
disruptions in urban transportation networks, can impair the dynamics crucial
for systems' functionality, such as electrochemical signals or human flows, or
any other type of information exchange, respectively, at larger topological
scales. Damage is usually modeled by progressive removal of components or
connections and, consequently, systems' robustness is assessed in terms of how
fast their structure fragments into disconnected sub-systems. Yet, this
approach fails to capture how damage hinders the propagation of information
across scales, since system function can be degraded even in absence of
fragmentation -- e.g., pathological yet structurally integrated human brain.
Here, we probe the response to damage of dynamical processes on the top of
complex networks, to study how such an information flow is affected. We find
that removal of nodes central for network connectivity might have insignificant
effects, challenging the traditional assumption that structural metrics alone
are sufficient to gain insights about how complex systems operate. Using a
damaging protocol explicitly accounting for flow dynamics, we analyze synthetic
and empirical systems, from biological to infrastructural ones, and show that
it is possible to drive the system towards functional fragmentation before full
structural disintegration.
