Due to its high efficiency, routing based on greedy embeddings of rooted spanning trees is a promising approach for dynamic, large-scale networks with restricted topologies. Friend-to-friend (F2F) overlays, one key application of embedding-based routing, aim to prevent disclosure of their participants to malicious members by restricting exchange of messages to mutually trusted nodes. Since embeddings assign a unique integer vector to each node that encodes its position in a spanning tree of the overlay, attackers can infer network structure from knowledge about assigned vectors. As this information can be used to identify participants, an evaluation of the scale of leakage is needed. In this work, we analyze in detail which information malicious participants can infer from knowledge about assigned vectors. Also, we show that by monitoring packet trajectories, malicious participants cannot unambiguously infer links between nodes of unidentified participants. Using simulation, we find that the vector assignment procedure has a strong impact on the feasibility of inference. In F2F overlay networks, using vectors of randomly chosen numbers for routing decreases the mean number of discovered individuals by one order of magnitude compared to the popular approach of using child enumeration indexes as vector elements.