Group Consensus in Multilayer Networks

While there has been considerable work addressing consensus and group consensus in single-layer networks, not much attention has been devoted to consensus in multilayer networks. In this paper, we fill this gap by considering multilayer networks consisting of agents of different types while agents of the same type are arranged in separate layers. The patterns of emerging group consensus are determined by the symmetries of the multilayer network. An analysis of these symmetries reveals a partition of the nodes in each layer into clusters where the nodes in each cluster may achieve group consensus. We show that it is possible for group consensus to arise independently of the particular dynamics of the agents, which may be stable, marginally stable, or unstable. The concept of isolated group consensus where certain clusters of nodes in the multilayer network achieve group consensus while others do not is also introduced.