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Résumé : In this paper, we study the probability that a network within a given geometry is fully connected. We consider two generic scenarios of practical importance to wireless communications, in which one or more nodes are located outside the convex space where the remaining nodes reside. Consequently, conventional approaches with the underlying assumption that only line-of-sight (LOS) or direct connections between nodes are possible, fail to provide the correct analysis for the connectivity. We present an analytical framework that explicitly considers the effects of reflections from the system boundaries on the full connection probability. A simple two-dimensional geometry is first considered, followed by a more practical three-dimensional system. The analysis presented can potentially be extended to networks residing in a number of non-convex geometries. To corroborate our derivations, we compare our theoretical results with simulated data. Furthermore, we analyze the effects of different system parameters on the connectivity of the network through simulation and analysis.