  Social networks are not static but rather constantly evolve in time. One of
the elements thought to drive the evolution of social network structure is
homophily - the need for individuals to connect with others who are similar to
them. In this paper, we study how the spread of a new opinion, idea, or
behavior on such a homophily-driven social network is affected by the changing
network structure. In particular, using simulations, we study a variant of the
Axelrod model on a network with a homophilic rewiring rule imposed. First, we
find that the presence of homophilic rewiring within the network, in general,
impedes the reaching of consensus in opinion, as the time to reach consensus
diverges exponentially with network size $N$. We then investigate whether the
introduction of committed individuals who are rigid in their opinion on a
particular issue, can speed up the convergence to consensus on that issue. We
demonstrate that as committed agents are added, beyond a critical value of the
committed fraction, the consensus time growth becomes logarithmic in network
size $N$. Furthermore, we show that slight changes in the interaction rule can
produce strikingly different results in the scaling behavior of $T_c$. However,
the benefit gained by introducing committed agents is qualitatively preserved
across all the interaction rules we consider.
