Full Connectivity: Corners, Edges and Faces

@article{Coon2012FullCC,
  title={Full Connectivity: Corners, Edges and Faces},
  author={Justin P. Coon and Carl P. Dettmann and Orestis Georgiou},
  journal={Journal of Statistical Physics},
  year={2012},
  volume={147},
  pages={758-778}
}
We develop a cluster expansion for the probability of full connectivity of high density random networks in confined geometries. In contrast to percolation phenomena at lower densities, boundary effects, which have previously been largely neglected, are not only relevant but dominant. We derive general analytical formulas that show a persistence of universality in a different form to percolation theory, and provide numerical confirmation. We also demonstrate the simplicity of our approach in… 
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63 Citations
Highly Influential Citations
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Background Citations
38
Methods Citations
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Results Citations
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63 Citations

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  • Computer Science
    2014 12th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks (WiOpt)
  • 2014
TLDR
A systematic methodology for analytically characterizing the connectivity probability when the network resides within a convex right prism, a polyhedron that accurately models many geometries that can be found in practice.
Dettmann, C. (2018). Isolation and connectivity in random geometric graphs
TLDR
It is shown that nonuniformity can break the Poisson distribution property, but it strengthens the link between isolation and connectivity, and stretches out the connectivity transition.
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