  To understand the controllability of complex networks is a forefront problem
relevant to different fields of science and engineering. Despite recent
advances in network controllability theories, an outstanding issue is to
understand the effect of network topology and nodal interactions on the
controllability at the most fundamental level. Here we develop a universal
framework based on local information only to unearth the most {\em fundamental
building blocks} that determine the controllability. In particular, we
introduce a network dissection process to fully unveil the origin of the role
of individual nodes and links in control, giving rise to a criterion for the
much needed strong structural controllability. We theoretically uncover various
phase-transition phenomena associated with the role of nodes and links and
strong structural controllability. Applying our theory to a large number of
empirical networks demonstrates that technological networks are more strongly
structurally controllable (SSC) than many social and biological networks, and
real world networks are generally much more SSC than their random counterparts
with intrinsic resilience and adaptability as a result of human design and
natural evolution.
