Exploring anti-community structure in networks with application to incompatibility of traditional Chinese medicine

Community structure is one of the most important properties in networks, in which a node shares its most connections with the others in the same community. On the contrary, the anti-community structure means the nodes in the same group have few or no connections with each other. In Traditional Chinese Medicine (TCM), the incompatibility problem of herbs is a challenge to the clinical medication safety. In this paper, we propose a new anti-community detection algorithm, Random non-nEighboring nOde expansioN (REON), to find anti-communities in networks, in which a new evaluation criterion, anti-modularity, is designed to measure the quality of the obtained anti-community structure. In order to establish anti-communities in REON, we expand the node set by non-neighboring node expansion and regard the node set with the highest anti-modularity as an anti-community. Inspired by the phenomenon that the node with higher degree has greater contribution to the anti-modularity, an improved algorithm called REONI is developed by expanding node set by the non-neighboring node with the maximum degree, which greatly enhances the efficiency of REON. Experiments on synthetic and real-world networks demonstrate the superiority of the proposed algorithms over the existing methods. In addition, by applying REONI to the herb network, we find that it can discover incompatible herb combinations.