Consensus in social networks with complex structure of social actors

We study opinion dynamics in network structures of a special type: each node consists of two agents interacting among themselves. The external agent interacts with the rest of the network and the internal agent interacts only with the external one. For example, every external agent has a personal advisor who doesn’t participate directly in the negotiations. We investigate properties of the consensus arising in these network structures under conventional de Groot opinion dynamics model and how the final influences depends on the mutual trust between external and internal agents. The analytical solution for the vector of final influences was obtained. We show that the final influence of a node depends monotonically on the trust between external and internal agents. It was shown for the two-node case under what conditions the internal parameters of a node are more important than the external ones. Our results can potentially be extended to the networks where nodes have more complex internal structure.