We present two novel distributed algorithms for hole detection in a wireless sensor network (WSN) based on the distributed Delaunay triangulation of the underlying communication graph. The first, which we refer to as the distance-vector hole determination (DVHD) algorithm, is based on traditional distance vector routing for multi-hop networks and shortest path lengths between node pairs. The second, which we refer to as the Gaussian curvature-based hole determination (GCHD) algorithm, applies the Gauss-Bonnet theorem on the Delaunay graph to calculate the number of holes based on the graph’s Gaussian curvature. We present a detailed comparative performance analysis of both methods based on simulations, showing that while DVHD is conceptually simpler, the GCHD algorithm shows better performance with respect to run-time and message count per node