  We introduce a contrarian opinion (CO) model in which a fraction p of
contrarians within a group holds a strong opinion opposite to the opinion held
by the rest of the group. At the initial stage, stable clusters of two
opinions, A and B exist. Then we introduce contrarians which hold a strong B
opinion into the opinion A group. Through their interactions, the contrarians
are able to decrease the size of the largest A opinion cluster, and even
destroy it. We see this kind of method in operation, e.g when companies send
free new products to potential customers in order to convince them to adopt the
product and influence others. We study the CO model, using two different
strategies, on both ER and scale-free networks. In strategy I, the contrarians
are positioned at random. In strategy II, the contrarians are chosen to be the
highest degrees nodes. We find that for both strategies the size of the largest
A cluster decreases to zero as p increases as in a phase transition. At a
critical threshold value p_c the system undergoes a second-order phase
transition that belongs to the same universality class of mean field
percolation. We find that even for an ER type model, where the degrees of the
nodes are not so distinct, strategy II is significantly more effctive in
reducing the size of the largest A opinion cluster and, at very small values of
p, the largest A opinion cluster is destroyed.
