Reconstructing complex networks with binary-state dynamics

The prerequisite for our understanding of many complex networked systems lies in the reconstruction of network structure from measurable data. Although binary-state dynamics occurring in a broad class of complex networked systems in nature and society and has been intensively investigated, a general framework for reconstructing complex networks from binary states, the inverse problem, is lacking. Here we offer a general solution to the reconstruction problem by developing a data-based linearization approach for binary-state dynamics with linear, nonlinear, discrete and stochastic switching functions. The linearization allows us to convert the network reconstruction problem into a sparse signal reconstruction problem that can be resolved efficiently and credibly by convex optimization based on compressed sensing. The completely data-based linearization method and the sparse signal reconstruction constitutes a general framework for reconstructing complex networks without any knowledge of the binary-state dynamics occurring on them in an extremely efficient and robust manner. Our framework has been validated by several different kinds of binary-state dynamics in combination with a large number of artificial and real complex networks. A universal high reconstruction accuracy is achieved in spite of the measurement noise and missing data of partial nodes. Our approach opens a new route to the inverse problem in complex networked systems with binary-state dynamics and improves our ability to fully understand and control their emergent dynamics in a comprehensive way.