  In the standard $q$-voter model, a given agent can change its opinion only if
there is a full consensus of the opposite opinion within a group of influence
of size $q$. A more realistic extension is the threshold $q$-voter, where a
minimal agreement (at least $0<q_0\le q$ opposite opinions) is sufficient to
flip the central agent's opinion, including also the possibility of independent
(non conformist) choices. Variants of this model including non-conformist
behavior have been previously studied in fully connected networks (mean-field
limit). Here we investigate its dynamics in random networks. Particularly,
while in the mean-field case it is irrelevant whether repetitions in the
influence group are allowed, we show that this is not the case in networks, and
we study the impact of both cases, with or without repetition. Furthermore, the
results of computer simulations are compared with the predictions of the pair
approximation derived for uncorrelated networks of arbitrary degree
distributions.
