The stated problem does not produce an acyclic graph. For instance, if A has B in their contacts, then B is not forbidden from having A in their contacts. In fact, by ensuring that for all A, if A has B as a contact, then B has A as a contact, we can eliminate directedness from the graph and, via isomorphism, pretend we are operating on an undirected graph.

The requirement that no actor forward a message twice is merely equivalent to finding a simple path through the graph. It does not “basically” mean there are no cycles.