Exploring node interaction relationship in complex networks by using high-frequency signal injection

Many practical systems can be described by complex networks. These networks produce, day and night, rich data which can be used to extract information from the systems. Often, output data of some nodes in the networks can be successfully measured and collected while the structures of networks producing these data are unknown. Thus, revealing network structures by analyzing available data, referred to as network reconstruction, turns to be an important task in many realistic problems. Limitation of measurable data is a very common challenge in network reconstruction. Here we consider an extreme case, i.e., we can only measure and process the data of a pair of nodes in a large network, and the task is to explore the relationship between these two nodes while all other nodes in the network are hidden. A driving-response approach is proposed to do so. By loading a high-frequency signal to a node (defined as node A), we can measure data of the partner node (node B), and work out the connection structure, such as the distance from node A to node B and the effective intensity of interaction from A to B, with the data of node B only. A systematical smoothing technique is suggested for treating noise problem. The approach has practical significance.