Identification of co-existing embeddings of a motif in multilayer networks

Interactions among molecules, also known as biological networks, are often modeled as binary graphs, where nodes and edges represent the molecules and the interaction among those molecules, such as signal transmission, genes-regulation, and protein-protein interactions. Subgraph patterns which are recurring in these networks, called motifs, describe conserved biological functions. Although traditional binary graph provides a simple model to study biological interactions, it lacks the expressive power to provide a holistic view of cell behavior as the interaction topology alters and adopts under different stress conditions as well as genetic variations. Multilayer network model captures the complexity of cell functions for such systems. Unlike the classic binary network model, multilayer network model provides an opportunity to identify conserved functions in cell among varying conditions. In this paper, we introduce the problem of co-existing motifs in multilayer networks. These motifs describe the dual conservation of the functions of cells within a network layer (i.e., cell condition) as well as across different layers of networks. We propose a new algorithm to solve the co-existing motif identification problem efficiently and accurately. Our experiments on both synthetic and real datasets demonstrate that our method identifies all co-existing motifs at near 100 % accuracy for all networks we tested on, while competing method's accuracy varies greatly between 10 to 95 %. Furthermore, our method runs at least an order of magnitude faster than state of the art motif identification methods for binary network models.