  In this paper, we propose a Boltzmann-type kinetic description of opinion
formation on social networks, which takes into account a general connectivity
distribution of the individuals. We consider opinion exchange processes
inspired by the Sznajd model and related simplifications but we do not assume
that individuals interact on a regular lattice. Instead, we describe the
structure of the social network statistically, assuming that the number of
contacts of a given individual determines the probability that their opinion
reaches and influences the opinion of another individual. From the kinetic
description of the system, we study the evolution of the mean opinion, whence
we find precise analytical conditions under which a \textit{polarisation
switch} of the opinions, i.e. a change of sign between the initial and the
asymptotic mean opinions, occurs. In particular, we show that a non-zero
correlation between the initial opinions and the connectivity of the
individuals is necessary to observe polarisation switch. Finally, we validate
our analytical results through Monte Carlo simulations of the stochastic
opinion exchange processes on the social network.
