  The understanding of how users in a network update their opinions based on
their neighbours opinions has attracted a great deal of interest in the field
of network science, and a growing body of literature recognises the
significance of this issue. In this research paper, we propose a new dynamic
model of opinion formation in directed networks. In this model, the opinion of
each node is updated as the weighted average of its neighbours opinions, where
the weights represent social influence. We define a new centrality measure as a
social influence metric based on both influence and conformity. We measure this
new approach using two opinion formation models: (i) the Degroot model and (ii)
our own proposed model. Previously published research studies have not
considered conformity, and have only considered the influence of the nodes when
computing the social influence. In our definition, nodes with low in-degree and
high out-degree that were connected to nodes with high out-degree and low
in-degree had higher centrality. As the main contribution of this research, we
propose an algorithm for finding a small subset of nodes in a social network
that can have a significant impact on the opinions of other nodes. Experiments
on real-world data demonstrate that the proposed algorithm significantly
outperforms previously published state-of-the-art methods.
