  We present an extensive study of the joint effects of heterogeneous social
agents and their heterogeneous social links in a bounded confidence opinion
dynamics model. The full phase diagram of the model is explored for two
different network's topologies and compared to two opposed extreme cases: on
one hand heterogeneous agents which constitute a mixed population and on the
other, their interactions are modeled by a lattice. The results show that when
agents prone to compromising coexist with close minded ones, the steady state
of the dynamics shows coexistent phases. In particular, unlike the homogeneous
case in networks, or the heterogeneous case in fully mixed population, it is
possible that the society ends up in consensus around one extreme opinion.
Moreover, during the dynamics, the consensus may be overturned from one extreme
to the other of the opinion space. We also show that the standard order
parameter, the normalized average size of the largest opinion cluster, may be
misleading in this case, as it hides the existence of these phases. The phase
where the opinion of the society is overturned does not require the presence of
agents with special characteristics, (stubborn, extremists, etc.); it results
from the interplay of agents which have agreed on an extreme opinion with the
remaining group that holds the opposite one. Among the former, some may be
prone to compromising with other agents which are out of the majority group,
these agents, according to their location in the network, may act like bridges
between the two groups and slowly attract the whole society to the other
extreme.
