Bipartite centrality diffusion: Mining higher-order network structures via motif-vertex interactions

Understanding network structures at the level of functional building blocks, also known as network motifs, is of crucial importance for many real-world applications. In this work, we develop a framework to model the interactions between high-order motif instances and graph nodes using a bipartite graph. The roles of motif instances can then be revealed via the latent feature embeddings resultant from the bipartite graph. In contrast to existing methods, our work is among the first attempts to explicitly study the relation between motif instances by bridging them naturally with the original nodes in the graph. Moreover, the proximity on the high-order centrality measure of motif instances and nodes are found to coincide with the high-order clustering organization in the networks. Our approach demonstrates significant performance on a number of real-world network datasets.