  Controlling complex networks is of paramount importance in science and
engineering. Despite the recent development of structural-controllability
theory, we continue to lack a framework to control undirected complex networks,
especially given link weights. Here we introduce an exact-controllability
paradigm based on the maximum multiplicity to identify the minimum set of
driver nodes required to achieve full control of networks with arbitrary
structures and link-weight distributions. The framework reproduces the
structural controllability of directed networks characterized by structural
matrices. We explore the controllability of a large number of real and model
networks, finding that dense networks with identical weights are difficult to
be controlled. An efficient and accurate tool is offered to assess the
controllability of large sparse and dense networks. The exact-controllability
framework enables a comprehensive understanding of the impact of network
properties on controllability, a fundamental problem towards our ultimate
control of complex systems.
