<p>Uncover the vertices of a given graph, deterministic or random, in uniformly random order; we consider both a discrete-time and a continuous-time version. We study the evolution of the number of visible edges, and show convergence after normalization to a Gaussian process. This problem was studied by Hackl, Panholzer, and Wagner for the case when the graph is a uniformly random labelled tree; we generalize their result to more general graphs, including both other classes of random and non-random trees, and denser graphs. The results are similar in all cases, but some differences can be seen depending on the size of the average degree and of the variance of the vertex degrees.</p>