Reconstruction and Layer Division of Unknown Multilayer Networks

Topology identification of multilayer networks is of great significance in the fields of information, engineering, and society. Current research on topology identification of multilayer networks requires the knowledge of the specific number of layers and the corresponding nodes in each layer in advance. However, the information is often unknown in reality. Herein, for a multilayer network with unknown layers, where node dynamic functions are in the quadratic form, we can obtain the specific layers and the topology structure based on compressive sensing. Notably, the number of layers can be obtained in two ways: 1) by the number of diverse node dynamic functions or 2) inner coupling matrices. The effectiveness and robustness of our method are verified through numerical simulations.