  Most people simultaneously belong to several distinct social networks, in
which their relations can be different. They have opinions about certain
topics, which they share and spread on these networks, and are influenced by
the opinions of other persons. In this paper, we build upon this observation to
propose a new nodal centrality measure for multiplex networks. Our measure,
called Opinion centrality, is based on a stochastic model representing opinion
propagation dynamics in such a network. We formulate an optimization problem
consisting in maximizing the opinion of the whole network when controlling an
external influence able to affect each node individually. We find a
mathematical closed form of this problem, and use its solution to derive our
centrality measure. According to the opinion centrality, the more a node is
worth investing external influence, and the more it is central. We perform an
empirical study of the proposed centrality over a toy network, as well as a
collection of real-world networks. Our measure is generally negatively
correlated with existing multiplex centrality measures, and highlights
different types of nodes, accordingly to its definition.
