High-order Organization of Weighted Microbial Interaction Network

High-order connectivity patterns are essential to understanding the basic structure of complex networks. Network motifs are considered as the basic building blocks of complex networks. From identifying network motifs to discovering higher-order modular organizations by them, it is helpful to study the organization principles and functional modules of the biological networks in a divide-and-conquer manner. However, the current research based on network motifs often neglect the influence of weight in network motifs. In this paper, the concept of weighted motifs was presented and was applied to microbial network. The method was proposed to find the optimal weighted motif in microbial network and analyze the high-order structure of weighted networks based on them. It also proved that the partially weighted motifs can obtain optimal clusters in theory over unweighted ones.