A two-stage reconstruction method for complex networked system with hidden nodes.

Reconstructing the interacting topology from measurable data is fundamental to understanding, controlling, and predicting the collective dynamics of complex networked systems. Many methods have been proposed to address the basic inverse problem and have achieved satisfactory performance. However, a significant challenge arises when we attempt to decode the underlying structure in the presence of inaccessible nodes due to the partial loss of information. For the purpose of improving the accuracy of network reconstruction with hidden nodes, we developed a robust two-stage network reconstruction method for complex networks with hidden nodes from a small amount of observed time series data. Specifically, the proposed method takes full advantage of the natural sparsity of complex networks and the potential symmetry constraints in dynamic interactions. With robust reconstruction, we can not only locate the position of hidden nodes but also precisely recover the overall network structure on the basis of compensated nodal information. Extensive experiments are conducted to validate the effectiveness of the proposed method and superiority compared with ordinary methods. To some extent, this work sheds light on addressing the inverse problem, of which the system lacks complete exploration in the network science community.