Embedding model of multilayer networks structure and its application to identify influential nodes

At present, there are many indexes used to quantify the structure of single layer complex networks, but multilayer networks are affected by the number of layers, which are difficult to represent the structure and complicated to calculate. In this paper, we propose a network embedding method to represent the structure information of multilayer networks, which reduces the computational complexity. After the structure of the multilayer networks is expressed, the key nodes in the network are mined to help control the spread of the epidemic, suppress the spread of rumors, and optimize the structure of the network. However, it is difficult to quantify this problem precisely because of the difference of judgment indexes. On the basis of representing the structure of multilayer networks, we propose a fuzzy Tsallis eXtropy (FTE) method for quantifying influential nodes in multilayer networks by combining fuzzy theory and entropy. In addition, FTE is tested by some practical networks and compared with other methods. The results reveal that the proposed method is effective.