In a random geometric graph points are randomly distributed in space, and each point is given a random radius. Two points are joined by an edge if their distance is smaller than the sum of the two radii. When such a random graph is conditioned to have more edges than it would normally have, the excess edges can form different geometries. For example, a small number of points could get a large radius and therefore be adjacent to a high number of edges, or points could accumulate in a small spatial area and form a complete graph by virtue of their proximity. The purpose of the project is to investigate the different geometric configurations arising in these condensing graphs in dependence on the distribution of the individual radii.