Percolation thresholds on planar Euclidean relative-neighborhood graphs.

  title={Percolation thresholds on planar Euclidean relative-neighborhood graphs.},
  author={Oliver Melchert},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  volume={87 4},
  • O. Melchert
  • Published 29 January 2013
  • Mathematics
  • Physical review. E, Statistical, nonlinear, and soft matter physics
In the present article, statistical properties regarding the topology and standard percolation on relative neighborhood graphs (RNGs) for planar sets of points, considering the Euclidean metric, are put under scrutiny. RNGs belong to the family of "proximity graphs"; i.e., their edgeset encodes proximity information regarding the close neighbors for the terminal nodes of a given edge. Therefore they are, e.g., discussed in the context of the construction of backbones for wireless ad hoc… 

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