  We study cluster assignment in multi-agent networks. We consider homogeneous
diffusive networks, and focus on design of the graph that ensures the system
will converge to a prescribed cluster configuration, i.e., specifying the
number of clusters and agents within each cluster. Leveraging recent results
from cluster synthesis, we show that it is possible to design an oriented graph
such that the action of the automorphism group of the graph has orbits of
predetermined sizes, guaranteeing that the network will converge to the
prescribed cluster configuration. We provide upper and lower bounds on the
number of edges that are needed to construct these graphs along with a
constructive approach for generating these graphs. We support our analysis with
some numerical examples.
