  The q-voter model, a variant of the classic voter model, has been analyzed by
several authors: while allowing to study opinion dynamics, this model is also
believed to be one of the most representative among the many defined in the
wide field of sociophysics. Here, we investigate the consequences of conformity
on the consensus reaching process, by numerically simulating a q-voter model
with agents behaving either as conformists or non-conformists, embedded on
heterogeneous network topologies (as small-world and scale-free). In fact,
although it is already known that conformity enhances the reaching of
consensus, the related process is often studied only on fully-connected
networks, thus strongly limiting our full understanding of it. This paper
represents a first step in the direction of analyzing more realistic social
models, showing that different opinion formation-phases, driven by the
conformist agents density, are observable. As a result, we identify threshold
values of the density of conformist agents, varying across different topologies
and separating different regimes of our system, ranging from a disordered
phase, where different opinions coexist, to a gradually more ordered phase,
where consensus is eventually reached.
