  Within the framework of a simple model for social influence, the Taylor
model, we analytically investigate the role of stubborn agents in the overall
opinion dynamics of networked systems. Similar to zealots, stubborn agents are
biased towards a certain opinion and have a major effect on the collective
opinion formation process. Based on a modified version of the network Laplacian
we derive quantities capturing the transient dynamics of the system and the
emerging stationary opinion states. In the case of a single stubborn agent we
characterize his/her ability to coherently change a prevailing consensus. For
two antagonistic stubborn agents we investigate the opinion heterogeneity of
the emerging non-consensus states and describe their statistical properties
using a graph metric similar to the resistance distance in electrical networks.
Applying the model to synthetic and empirical networks we find while opinion
diversity is decreased by small-worldness and favored in the case of a
pronounced community structure the opposite is true for the coherence of
opinions during a consensus change.
