A Method for Computing the Minimum Common Feedback Set for a Multilayer Network and Its Application to Analysis of Biological Data

Network theory has been applied in fields such as social networks to extract important information, and various graph theoretic concepts have been utilized. At the same time, it has also been applied to biological data. One widely applied concept is the feedback vertex set (FVS), which is useful for identifying driver nodes for network control in single-layer networks, with the problem of finding the minimum feedback vertex set (MFVS) being important for determining the smallest number of driver nodes. Recently, multilayer networks are being used to represent biological data as well as single-layer networks. In this paper, we study the minimum common feedback vertex set (MCFVS) as an extension of MFVS for multilayer networks and develop an integer linear programming-based method for computing MCFVS. In order to efficiently handle larger networks, we further introduce graph compression and cycle detection methods. To examine the usefulness of MCFVS, we compare the number of elements in the MCFVS to the number of elements in the sum set (Union) of the MFVS for each layer using artificially generated networks and real biological networks. The results suggest that MCFVS may offer fewer driver nodes than traditional methods, such as Union.