  Adaptive networks consist of a collection of agents with adaptation and
learning abilities. The agents interact with each other on a local level and
diffuse information across the network through their collaborations. In this
work, we consider two types of agents: informed agents and uninformed agents.
The former receive new data regularly and perform consultation and in-network
tasks, while the latter do not collect data and only participate in the
consultation tasks. We examine the performance of adaptive networks as a
function of the proportion of informed agents and their distribution in space.
The results reveal some interesting and surprising trade-offs between
convergence rate and mean-square performance. In particular, among other
results, it is shown that the performance of adaptive networks does not
necessarily improve with a larger proportion of informed agents. Instead, it is
established that the larger the proportion of informed agents is, the faster
the convergence rate of the network becomes albeit at the expense of some
deterioration in mean-square performance. The results further establish that
uninformed agents play an important role in determining the steady-state
performance of the network, and that it is preferable to keep some of the
highly connected agents uninformed. The arguments reveal an important interplay
among three factors: the number and distribution of informed agents in the
network, the convergence rate of the learning process, and the estimation
accuracy in steady-state. Expressions that quantify these relations are
derived, and simulations are included to support the theoretical findings. We
further apply the results to two models that are widely used to represent
behavior over complex networks, namely, the Erdos-Renyi and scale-free models.
