  To understand, predict, and control complex networked systems, a prerequisite
is to reconstruct the network structure from observable data. Despite recent
progress in network reconstruction, binary-state dynamics that are ubiquitous
in nature, technology and society still present an outstanding challenge in
this field. Here we offer a framework for reconstructing complex networks with
binary-state dynamics by developing a universal data-based linearization
approach that is applicable to systems with linear, nonlinear, discontinuous,
or stochastic dynamics governed by monotonous functions. The linearization
procedure enables us to convert the network reconstruction into a sparse signal
reconstruction problem that can be resolved through convex optimization. We
demonstrate generally high reconstruction accuracy for a number of complex
networks associated with distinct binary-state dynamics from using binary data
contaminated by noise and missing data. Our framework is completely data
driven, efficient and robust, and does not require any a priori knowledge about
the detailed dynamical process on the network. The framework represents a
general paradigm for reconstructing, understanding, and exploiting complex
networked systems with binary-state dynamics.
