We analyze graphs in which each vertex is assigned random coordinates in a geometric space of arbitrary dimensionality and only edges between adjacent points are present. The critical connectivity is found numerically by examining the size of the largest cluster. We derive an analytical expression for the cluster coefficient, which shows that the graphs are distinctly different from standard random graphs, even for infinite dimensionality. Insights relevant for graph bipartitioning are included.

• Received 4 March 2002

DOI:https://doi.org/10.1103/PhysRevE.66.016121