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.

中文翻译：

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多层网络中的群体共识

虽然在单层网络中已经有大量的工作来解决共识和群体共识，但对多层网络中的共识却没有太多关注。在本文中，我们通过考虑由不同类型的代理组成的多层网络来填补这一空白，而相同类型的代理则排列在不同的层中。新兴群体共识的模式由多层网络的对称性决定。对这些对称性的分析揭示了将每一层中的节点划分为集群，其中每个集群中的节点可以达成群体共识。我们表明，群体共识有可能独立于代理的特定动态而产生，这些动态可能是稳定的、边缘稳定的或不稳定的。