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1 results

  • Point-based polygonal models for random graphs

  • Part of
  • T. Arak, P. Clifford, D. Surgailis
  • Journal:
    Advances in Applied Probability / Volume 25 / Issue 2 / June 1993
    Published online by Cambridge University Press:
    01 July 2016, pp. 348-372
    Print publication:
    June 1993

  • We define a class of two-dimensional Markov random graphs with I, V, T and Y-shaped nodes (vertices). These are termed polygonal models. The construction extends our earlier work [1]– [5]. Most of the paper is concerned with consistent polygonal models which are both stationary and isotropic and which admit an alternative description in terms of the trajectories in space and time of a one-dimensional particle system with motion, birth, death and branching. Examples of computer simulations based on this description are given.