Networks

    Random geometric networks consist of a collection of entities called nodes distributed randomly in a region, with pairwise connections that exist with a probability depending on the distance between the nodes. They are important in wireless communications and in many other contexts. We study the probability that the network as a whole is completely connected and how this depends on the shape of the region, developing a systematic perturbation expansion. It turns out that boundaries are very important, and can be characterised in terms of individual components such as corners, edges and faces; this is confirmed numerically.

  1. Impact of boundaries on fully connected random geometric networks, J. P. Coon, C. P. Dettmann and O. Georgiou, Phys. Rev. E 85 011138 (2012). pdf arxiv
  2. Full Connectivity: Corners, edges and faces, J. P. Coon, C. P. Dettmann and O. Georgiou, J. Stat. Phys. 147 758-778 (2012). pdf arxiv poster
  3. On the connectivity of 2-D random networks with anisotropically radiating nodes, J. P. Coon and C. P. Dettmann, IEEE Commun. Lett. 17 321-324 (2013). pdf
  4. An approximation of the Marcum Q-function with application to the performance analysis of communication systems, M. Z. Bocus, C. P. Dettmann and J. P. Coon, IEEE Commun. Lett. (to appear). arxiv
  5. Connectivity of confined dense networks: Boundary effects and scaling laws, J. P. Coon, C. P. Dettmann and O. Georgiou, submitted pdf arxiv
  6. Keyhole and Reflection Effects in Network Connectivity Analysis, M. Z. Bocus, C. P. Dettmann, J. P. Coon, M. R. Rahman, submitted arxiv.
  7. Proceedings: Towards k-connectivity: Local and global approaches, O. Georgiou, C. P. Dettmann and J. P. Coon (submitted) pdf

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