  Entanglement-based quantum networks exhibit a unique flexibility in the
choice of entangled resource states that are then locally manipulated by the
nodes to fulfill any request in the network. Furthermore, this manipulation is
not uniquely defined and thus can be optimized. We tailor the adaptation of the
resource state or pre-established entanglement to achieve bipartite
communication in an imperfect setting that includes time-dependent memory
errors. In this same setting, we study how the flexibility of this approach can
be used for the distribution of entanglement in a fully asymmetric network
scenario. The considered entanglement topology is a custom one based on the
minimization of the required measurements to retrieve a Bell pair. The
optimization of the manipulation and the study of such a custom entanglement
topology are performed using the noisy stabilizer formalism, a recently
introduced method to fully track noise on graph states. We find that exploiting
the flexibility of the entanglement topology, given a certain set of bipartite
requests, is highly favorable in terms of the fidelity of the final state.
