Motif importance measurement based on multi-attribute decision

Complex network is an important tool for studying complex systems. From the mesoscopic perspective, the complex network is composed of a large number of different types of motifs, research on the importance of motifs is helpful to analyse the function and dynamics of a complex network. However, the importance of different motifs or the same kind of motifs in the network is different, and the importance of motifs is not only affected by a single factor. Therefore, we propose a comprehensive measurement method of motif importance based on multi-attribute decision-making (MAM). We use the idea of MAM and take into account the influence of the local attribute, global attribute and location attribute of the motif on the network structure and function, and the information entropy method is used to give different weight to different attributes, finally, a comprehensive importance measure of the motif is obtained. Experimental results on the artificial network and real networks show that our method is more direct and effective for a small network.