2002/03/31 by Jesper Dall, Michael Christensen · 3 citations
Physics and Astronomy · #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.66.016121
published as Phys. Rev. E 66, 016121 (2002) · 16 pages, 10 figures. Minor changes. Added references
arxiv created 2002/05/08 · arxiv updated 2009/11/30
We analyse 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 bi-partitioning are included.