This paper proposes a network model of opinion dynamics based on both the social network structure and network centralities. The conceptual novelty in this model is that the opinion of each individual is weighted by the associated network centrality in characterizing the opinion spread on social networks. Following a degree-centrality-weighted opinion dynamics model, we provide an algorithm to partition nodes of any graph into two and multiple clusters based on opinion disagreements. Furthermore, the partition algorithm is applied to real-world social networks including the Zachary karate club network [1] and the southern woman network [2] and these application examples indirectly verify the effectiveness of the degree-centrality-weighted opinion dynamics model. Finally, properties of general centrality-weighted opinion dynamics model are established.