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Within the framework of a simple model for social influence, the Taylormodel, we analytically investigate the role of stubborn agents in the overallopinion dynamics of networked systems. Similar to zealots, stubborn agents arebiased towards a certain opinion and have a major effect on the collectiveopinion formation process. Based on a modified version of the network Laplacianwe derive quantities capturing the transient dynamics of the system and theemerging stationary opinion states. In the case of a single stubborn agent wecharacterize his/her ability to coherently change a prevailing consensus. Fortwo antagonistic stubborn agents we investigate the opinion heterogeneity ofthe emerging non-consensus states and describe their statistical propertiesusing a graph metric similar to the resistance distance in electrical networks.Applying the model to synthetic and empirical networks we find while opiniondiversity is decreased by small-worldness and favored in the case of apronounced community structure the opposite is true for the coherence ofopinions during a consensus change.

A Laplacian Approach to Stubborn Agents and their Role in Opinion Formation on Influence Networks