This article considers the challenge of recovering an initial topology of a mesh of devices based on noisy and incomplete measurements of their inter-distances. In comparison to earlier approaches, this paper provides a first guess of the topology, as opposed to recovering a precise geometry of each device. Using a graph-based model of the problem and properties of the 2D and 3D simplices, we show: (a) a topologically correct solution can be recovered when the solution is unique; (b) we can identify which vertices cannot be recovered and why, using a graph structure; and (c) the challenges due to local symmetries in making the solution nonunique. Results in simulation and with a mesh of UWB anchors demonstrate the applicability of the approach.