Wang Xinyu, Zhang Zhaoyang, Li Haihong, Chen Yang, Mi Yuanyuan, Hu Gang
School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China.
Department of Physics, School of Physical Science and Technology, Ningbo University, Ningbo, Zhejiang 315211, China.
Phys Rev E. 2021 Feb;103(2-1):022317. doi: 10.1103/PhysRevE.103.022317.
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.
许多实际系统都可以用复杂网络来描述。这些网络日夜产生丰富的数据，可用于从系统中提取信息。通常，网络中某些节点的输出数据能够成功测量和收集，但产生这些数据的网络结构却未知。因此，通过分析可用数据来揭示网络结构，即网络重构，在许多实际问题中成为一项重要任务。可测量数据的局限性是网络重构中一个非常常见的挑战。在此我们考虑一种极端情况，即我们只能测量和处理大型网络中一对节点的数据，任务是探索这两个节点之间的关系，而网络中的所有其他节点都是隐藏的。为此提出了一种驱动 - 响应方法。通过向一个节点（定义为节点A）加载高频信号，我们可以测量其伙伴节点（节点B）的数据，并仅利用节点B的数据计算出连接结构，如从节点A到节点B的距离以及从A到B的有效相互作用强度。建议采用一种系统的平滑技术来处理噪声问题。该方法具有实际意义。
