Abstract
Inferring network structures from available data has attracted much interest in network science; however, in many realistic networks, only some of the nodes are perceptible while others are hidden, making it a challenging task. In this work, we develop a method for reconstructing the network with hidden nodes and links, taking account of fast-varying noise and time-delay interactions. By calculating the correlations of available data with different derivative orders for multiple pairs of accessible nodes, analyzing and integrating the relationships between different correlations, and defining diverse hidden-node-related reconstruction motifs, we can effectively identify the hidden nodes and hidden links in the network.
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Gang Hu was supported by the National Natural Science Foundation of China (Grant No. 11835003). Zhaoyang Zhang was supported by the National Natural Science Foundation of China (Grant Nos. 12375033, 12235007, and 11975131), the Natural Science Foundation of Zhejiang (Grant No. LY23A050002), and the K. C. Wong Magna Fund at Ningbo University. Yuanyuan Mi was supported by the National Natural Science Foundation of China (Grant No. T2122016), the National Science and Technology Innovation 2030 Major Program (Grant Nos. 2021ZD0203700, and 2021ZD0203705), the Fundamental Research Funds for the Central Universities (Grant No. 2022CDJKYJH034). Zhilin Qu was supported by the National Institutes of Health (Grant Nos. R01 HL134709, R01 HL139829, R01 HL157116, and P01 HL164311). Yang Chen was supported by the National Natural Science Foundation of China (Grant No. 11905291), and CAS Project for Young Scientists in Basic Research (Grant No. YSBR-041).
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Zhang, Z., Wang, X., Li, H. et al. Uncovering hidden nodes and hidden links in complex dynamic networks. Sci. China Phys. Mech. Astron. 67, 240511 (2024). https://doi.org/10.1007/s11433-023-2303-7
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DOI: https://doi.org/10.1007/s11433-023-2303-7