P19

## Condensation in random geometric graphs

### Description

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.