  In this paper we propose an extended version of the Friedkin-Johnsen (FJ)
model that accounts for the effects of homophily mechanisms on the agents'
mutual appraisals. The proposed model consists of two difference equations. The
first one describes the opinions' evolution, namely how agents modify their
opinions taking into account both their personal beliefs and the influences of
other agents, as in the standard FJ model. Meanwhile, the second equation
models how the influence matrix involved in the opinion formation process
updates according to a homophily mechanism, by allowing both positive and
negative appraisals. We show that the proposed time-varying version of the
classical FJ model always asymptotically converges to a constant solution.
Moreover, in the case of a single discussion topic, the asymptotic behavior of
the system is derived in closed form.
